# Probability Problems On Balls With Solutions

----- Solution 2----- This problem can be solved using the concept of Conditional Probability Let A be the event of getting a Queen in the first draw Total number of Queens = 4. An urn contains 1 red ball and 10 blue balls. Putting the Ball In Your Court With Cancer Coaches. it's simple , there is a bucket that contains 5 red balls and 3 white balls , a player picks up 4 balls out of the bucket without returning any. What is my expected value of lateness? Answer: The problem tells us that we have the following. Find 9 Answers & Solutions for the question A bag contains 10 white, 4 green balls. Urn 1 contains white balls and red balls. An urn contains 6 red and 5 pink balls. You can solve many simple probability problems just by knowing two simple rules: The probability of any sample point can range from 0 to 1. If you're seeing this message, it means we're having trouble loading external resources on our website. If a man selects 2 balls at random from the bag,what is. Then read the problem again, slowly and carefully, to identify what the problem is asking. Many physics problems on dynamics with free detailed solutions. Students can also draw pictures to help them solve the problem. In a sample of 500 items, 120 are found to be defective. Since the first ball drawn was blue, for the second draw there are only 49 blue balls in the pot, so the probability of drawing a second blue ball is 49/99. The site consists of an integrated set of components that includes expository text, interactive web apps, data sets, biographical sketches, and an object library. Solutions to Exercises Marked with s from the book Introduction to Probability by Joseph K. 2) December 4, 2013 We can think of this problem as similar to Exercise 40. Pitman Stat 20 (white j at least one of two balls drawn was The answers are di erent because in c. Suppose the green ball goes in bin , for some. Drop balls through a triangular grid of pegs and see them accumulate in containers. A bag contains 3 red balls, 4 blue balls and 1 yellow ball, all the balls being identical in shape and size. The ball lands in the garden '24 004B 50 ft 16. A bag contains 1 Green ball, 2 Blue balls, and 1 White ball. NCERT Exemplar Problems Class 10 Maths - Statistics and Probability August 19, 2019 by Bhagya 3 Comments CBSETuts. If I'm interested in the suit of the card, there are four possible outcomes and the sample space is. Probability and Statistics Games: Probability Game Probability Problems with Alphabets Probability Activity with Spinner Permutations Math Topics Probability Quizzes: Probability and Statistics Quiz Probability and Statistics Quiz 3rd Grade Probability Quiz Ratio Quiz What is the Probability?. This is compound probability which means you are going to multiply each probability as you get it. Use manipulatives if needed. Throw a dice 3 times. Probability problems for aptitude pdf download, probability problems and solutions for aptitude, probability problems, random variables and probability distributions problems and solutions, probability word problems with solutions and answers, probability distribution problems and solutions, probability problems on balls with solutions, basic. The ball lands in the pool. Two balls are then drawn in succession. One is Green, one is Black and the other two are Yellow. What fraction of the large by. and also prepare you well for companies Like TCS, Infosys. Keywords: Urn problems, drawing without replacement, enumerative combinatorics, Scrabble, R. Discrete Probability The problems in this section are all computer programs. 2 Five white balls and ve black balls are. Ball and urn problem using Bayes theorem, probability to get a white ball. Suitable for KS4 students who are ready for something a little more challenging than the standard GCSE style question. The probability that 5 of them are pink and the rest are orange is a. Thus Nis a geometric rather than a Pascal random variable. Marcus Rashford and Anthony Martial could not strike up a connection during Man Utd's defeat by Bournemouth. The simulation will graph the average calculated probability of each class size. It follows simply from the axioms of conditional probability, but can be used to powerfully reason about a wide range of problems involving belief updates. The addresses of the first three houses were 296 Boo Blvd, 300 Boo Blvd and 304 Boo Blvd, and the house numbers continued to increase by 4 down the. Let the number of blue balls be x Therefore, Total no. ICSE Solutions for Class 10 Mathematics - Probability ICSE SolutionsSelina ICSE Solutions Get ICSE Solutions for Class 10 Mathematics Chapter 20 Probability for ICSE Board Examinations on APlusTopper. A biased coin (with probability of obtaining a Head equal to p > 0) is tossed repeatedly and independently until the ﬁrst head is observed. Probability: Solved 73 Probability Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. Two balls are chosen from the jar, with replacement. com community of teachers, mentors and students just like you that can answer any question you might have on Math. Probability distribution problems solutions pdf Random variables and their probability distributions can save us significant. Blitzstein and Jessica Hwang c Chapman & Hall/CRC Press, 2014 Joseph K. CHAPTER 3: PROBABILITY TOPICS. Then f′ (u)=−2u−3, and g′ (x)=−sinx–cosx. Students calculate the probability of pulling a variety of ball combinations out of a bag based on the total number of each. Definition: The probability that Y takes on the value y, P(Y=y), is defined as the sum of the probabilities of all points in S that are assigned the value y. Collections Etc. Learn how to apply Bayes Theorem to find the conditional probability of an event when the "reverse" conditional probability is the probability that is known. Problems,children's solutions,interactivities,games,articles,news. Probability and Statistics Games: Probability Game Probability Problems with Alphabets Probability Activity with Spinner Permutations Math Topics Probability Quizzes: Probability and Statistics Quiz Probability and Statistics Quiz 3rd Grade Probability Quiz Ratio Quiz What is the Probability?. We can solve this problem using the multiplication principle. This banner text can have markup. You have 50 white balls and 50 black balls. 3 Hole analysis to identify potential errant golf ball issues for only $299. There are two empty bowls in a room. Puzzle #1: Chances of Having Same Birthday Problem How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?. Tutorial on finding the probability of an event. The expected value is what you should anticipate happening in the long run of many trials of a game of chance. You also need to keep track of the time. Blitzstein and Jessica Hwang Departments of Statistics, Harvard University and Stanford University. Learn More Drug Problem The cooking Drug Rehab Center going to be of a good conventional as well as a great dinner expertise for rehab high seas Drug Rehab certainly be anyone to remember. Solution:1/4 P. Object Picking Probability - Sample Math Practice Problems The math problems below can be generated by MathScore. Whatever the problem, there’s a coach who can offer help. For example, in the above problem it tells us the probability of the both balls being the same color is 0. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same colour? (b) of different colours? Repeat under the. Probability Questions with Solutions. A second urn contains 16 red balls and an unknown number of blue balls. You must turn them in to me via a physical copy. The probability the 2nd ball drawn is one of your remaining 5 numbers is 5/39, since only 39 balls are left. If the two sides do not balance out, the lightest ball is clearly one of the 3 balls on the less weighted side. has pulled together a wonderful variety of problem-solvers that can help you address common household concerns, with a wide range of options for addressing storage, organization, cleaning, automotive, home security and more. To find the desired probability, we need to find P(X > 6) = 1 − P(X ≤ 6), which can be determined readily using the c. Putting the Ball In Your Court With Cancer Coaches. Its goal is to help the student of probability theory to master the theory more pro­ foundly and to acquaint him with the application of probability theory methods to the solution of practical problems. Probability Lessons Topics: Probability scale, Expected frequency, Bags of balls, Mutually exclusive events, Possibility space diagrams, Independent events, Balls in bag problems with two picks, Tree diagrams, Without replacement problems. Probability is finding the possible number of outcomes of the event occurrence. Each of the Strategic Practice documents here contains a set of strategic practice problems, solutions to those problems, a homework assignment, and solutions to the homework assignment. 6 Problem 1E. A ball is drawn and replaced with a ball of a diﬀerent colour. 1 day ago · Jim: Hi Reinhard. Latrease bought two hot dogs and a soda for a total of$7. Percent Word Problems Handout Revised @2009 MLC page 3 of 8 Percent Word Problems Directions: Set up a basic percent problem. An urn contains n red and m black balls. In a sample of 500 items, 120 are found to be defective. My HR Department insists that I rate my small staff (5 people) on a bell curve--one in the top 5% of all employees, one in the next 20%, one in the next 50%, one in the next 20%, and one in the bottom 5%. If the two sides do not balance out, the lightest ball is clearly one of the 3 balls on the less weighted side. You can only upload photos smaller than 5 MB. To find this probability, we need to transform the random variable (p 1 - p 2) into a z-score. Two balls are drawn at show more 1)A bag contains 2 red balls, 3 blue balls and 4 green balls. Suppose I draw a card from a standard deck of playing cards. The probability the 2nd ball drawn is one of your remaining 5 numbers is 5/39, since only 39 balls are left. What is the probability the two sums are 390 apart? I think the sum would come close to a normal distribution. Senior Army leaders said they’ve learned lessons from the problems with privatized housing that can be applied to prevent similar failures in privatizing any quality of life program. Suppose that two balls be randomly drawn, one after another, are to Solution: We must check whether or not. You now continue drawing balls on the assumption you did not draw a red. We also discuss some applications of probability theory to computing, including systems for making likely inferences from data and a class of useful algorithms that work "with high probability" but are not guaranteed to work all the time. The maths for doing probabilites goes like this. Avoid damage to property, persons, reputation, litigation. Problems and Complete explanatory solutions to problems on probability involving drawing, picking, selecting, choosing two or more balls from a box, bag, urn, container. 2 Counting Assignments One of the simplest but most important counting problems deals with a list of. 1) A student earned a grade of 80% on a math test that had 20 problems. Problem 34. 2 Multiple Choice Identify the choice that best completes the statement or answers the question. Find materials for this course in the pages linked along the left. Suppose he chooses B with probability p and C otherwise. We randomly pick a ball. Each time you pick two balls from the bin - the first ball and the second ball, both uniformly at random and you paint the second ball with the colour of the. The ball selected is not replaced and a second ball is selected at random from the same urn. Probability And Random Processes : Problems And Solutions. Let X be the number of red balls you pull before any black one, and Y the. Problem: A candidate is selected for interview for 3 posts. If the 2 sides balance out, you have found the lightest ball (the one set aside). How many students were in each bus? 2) Aliyah had $24 to spend on seven pencils. Possibility Spaces. • Probability and Statistics for Engineering and the Sciences by Jay L. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag. We can solve this problem using the multiplication principle. ____ 1 In a game, Erin is rolling a fair number cube with faces numbered 1 through 6. They will learn how to describe the probability of an event using numbers from 0 to 1. In this paper, we are concerned with the global structure of radial positive solutions of boundary value problem div(ϕN(∇v))+λf(|x|,v)=0inB(R),v=0on∂B(R), where ϕN(y)=y1−. Solutions, too, time permitting. No Questions Answer 1. Show that the probability of drawing a white ball now does not depend on k. Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. The problem is that if there are 3 balls in each urn, and you switch urns, then you get the same solution 2 Reducing Problems to Balls and Urns Q1: How many di erent con gurations are there in Tow-ers of Hanoi with n rings? A: The urns are the poles, the balls are the rings. Those balls corresponding to problems studied by the student are colored. Most of us miss this thing. The value 0. This Probability Pdf we are Providing is free to download. For example, if we pick 2 marbles from a bag there are different possibilities of what we could do: • Probability With Replacement We take a marble put it back into the bag and pick another one. Rohan takes a ball from the bag without looking into it. The probability of an offspring being a non-crested male is 4/16, which can be simplified to 1/4 or 25%. This is a famous paradox probability riddle which has caused a great deal of argument and disbelief from many who cannot accept the correct answer. Bag i contains i blue balls and 2 green balls. for the probabilities of the events for parts a through j. If the balls are drawn without replacement, then after every draw there will be one fewer ball in the pot, so the total number of balls for the second draw is 99. a Exactly one white ball is selected. (this problem is harder than what would be on the exam, but it is a useful application of probability for those interested in genetics) Each hereditary trait in an offspring depends on a pair of genes, one contributed by the father and the other by the mother. If a man selects 2 balls at random from the bag,what is the probability that he will get one ball of each colour? Algebra -> Probability-and-statistics -> SOLUTION: a bag contains 8 balls of which 5 are red and 3 are white. You can solve many simple probability problems just by knowing two simple rules: The probability of any sample point can range from 0 to 1. This occurs with proba-bility k n p. 9 Number of Heads Probability Probability ways these outcomes can occur. Frequently asked simple and hard probability problems or questions with solutions on cards, dice, bags and balls with replacement covered for all competitive exams,bank,interviews and entrance tests. Even though we discuss two events (usually labeled A and B), we’re really talking about performing one task (rolling dice, drawing cards, spinning a spinner, etc. Contribute to RodneyShag/HackerRank_solutions development by creating an account on GitHub. Homework solution 3 for APPM4/5560 Markov Process that are 0 or 1 with probability 1/2 each. Using the formula, P(R jB 1) = P(R. If it survives, we know the solution is in the top half of the building (floor 51 – 100). it's simple , there is a bucket that contains 5 red balls and 3 white balls , a player picks up 4 balls out of the bucket without returning any. b) Let q and e be next to each other as qe. You need at most one of the three textbooks listed below, but you will need the statistical tables. However, if the first ball was red, there will be 1 red and 2 blue balls left so the probability the second ball is blue is 2/3. Total number of balls = (2 + 3 + 2) = 7. Ball and urn problem using Bayes theorem, probability to get a white ball. This occurs with probability k n q. probability of selecting a blue and then a red ball is 0. What are the 4 solutions of this easy number puzzle? None of the students can have numbers 1 or 10, since they would guess the other one's number with no problems. Welcome to the Fresh Preserving newsletter! By signing up, you can expect to regularly receive news, tips, and discounts. Ask Math Questions you want answered. Now let Ji be the indicator of the event that the i’th red ball is pulled between the ﬁrst and the second black one. In a school of 1800 students, there are 875 girls. Problem: Solution: 1: Spin a spinner numbered 1 to 7, and toss a coin. Answer: A 35) A) 1 9 B) 4 12 = 1 3 C) 2 12 = 1 6 D) 2 9 E) none of these Solve the problem. Probability 381. (Note that you cannot find numerical answers here. Suppose that 7 green balls and 14 purple balls are placed in an urn. HW 7 + Solutions¶ Due Friday, August 13: Problems 7. In the case of a coin, there are maximum two possible outcomes - head or tail. Problems,children's solutions,interactivities,games,articles,news. Because we are drawing with replacement, the outcome of the second draw does not depend on the outcome of the first. Notice in this problem we are not dealing with the sum of both dice. The ball does not land in the pool. Solution 2 (more formal). The probability that any randomly chosen 2 people share the same birthdate. These operations with events are easily represented via Venn’s diagrams. The correct reasoning is to calculate the conditional probability. The probability of A, B, C solving a problem are 1/3, 2/7, and 3/8 respectively. What is the probability of the event that the last ball drawn is black?. A diagram of a communication network is shown. The conditional probability of an event is the probability that the event will occur given the knowledge that an event has already occurred. The text-books listed below will be useful for other courses on probability and statistics. - Analyze and interpret data sets. Find the probability of selecting a red ball. probability problems, probability, probability examples, how to solve probability word problems, probability based on area, examples with step by step solutions and answers, How to use permutations and combinations to solve probability problems, How to find the probability of of simple events, multiple independent events, a union of two events. Watch the best videos and ask and answer questions in 144 topics and 12 chapters in Algebra. Find the probability that the total of the. Probability is a measure of the likelihood that an event will occur. Set books The notes cover only material in the Probability I course. What is the probability of winning the National Lottery? The number of ways of choosing 6 numbers from 49 is 49 C 6 = 13 983. This page intentionally left blank. Probability Problems Ask A Question. In this problem, there is a tendency to reason that since the opposite face is either heads or tails, the desired probability is 1/2. We randomly draw a ball from the first bag and put it into the second bag. Probability Questions are provided with detailed answers to every question. Wasn’t sure how it would go or if they’d solve it. The pages that follow contain “unofﬁcial” solutions to problems appearing on the comprehensive exams in analysis given by the Mathematics Department at the University of Hawaii over the period from 1991 to 2007. Thus it is obtained by mixing two binomial probabilities: The following is the conditional probability : Thus _____ Answers for Problem 2. Compute the probability of randomly drawing five cards from a deck and getting exactly one Ace. A FIRST COURSE IN PROBABILITY. Conditional Probability and the Multiplication Rule Example An urn contains 3 red and 5 green balls. The computer simulation, which takes just a few seconds to run,. is neither affiliated with this site, nor with authors of this site. A ball is drawn 5 times from the bag containing the two balls. By Deborah J. Suppose we have two hats: one has 4 red balls and 6 green balls, the other has 6 red and 4 green. i am doubting my solution to this problem , therefore i hope someone assists me a bit. Do that twice. If two balls are to be choosen from 3 red balls and 2 white balls, what is the probability of picking at least one white ball? Answer: probability of picking at least one white ball is 1 - (probability of picking only red ball) 1 - ( 3C2/5C2) = 1- (3/10) = 7/10. Category B: Problems based on fundamental principal of counting and permutations and combinations. 2 Sample Space and Probability Chap. This fun game allows students to earn tokens to the fair by demonstrating their understanding of probability. Howson, for example, argues that “ Inductive reasoning is justified to the extent that it is sound, given appropriate premises ” (Howson 2000: 239, his emphasis). An experiment is conducted where these two balls are placed in a bag before drawing a ball out. Then EIi = 1 m+1, simply the probability that in a random ordering of the i’th red balls and all m black ones, the red comes ﬁrst. What is Bayes' Theorem? Bayes' theorem is a way to figure out conditional probability. Solutions to Miscellaneous Problems from Probability by J. Which also lets you compute the probability that your AGI will solve all the unknown problems too (assuming problem probabilities are independent). Drop balls through a triangular grid of pegs and see them accumulate in containers. Understand conditional probability. Solved examples with detailed answer description, explanation are given and it would be easy to understand - Page 3. Going back to our problem: In a bag, there are 10 red and green balls that are numbered from 11 to 20. Therefore, P(red)=. A ball is drawn from an urn containing 3 white and 3 black balls. Free student math practice. These problems are aimed at junior high and high school students with a flare for mathematics and logic. One is Green, one is Black and the other two are Yellow. If a red ball is drawn, what is the probability that it comes from the first urn? Solution In probabilistic terms, what we know about this problem can be formalized as follows: The unconditional probability of drawing a red ball can be derived using the law of total probability: By using Bayes' rule, we obtain. Calculation of probabilities of drawing objects (balls, beads, cards, etc. Compute P(BjA). balls and 4 green balls in a container. Set books The notes cover only material in the Probability I course. Proceed to the next problem by clicking the broom icon. Slader is an independent website supported by millions of students and contributors from all across the globe. I have done my best to ensure that the solutions are clear and correct, and that the level of rigor is at least as high as that. How to solve probability problems. 45 which is around 55%. – This problem is from beanactuary. Four balls are randomly drawn from the urn in succession, with replacement. Thus the probability that the green ball goes in bin , and the red ball goes in a bin greater than , is. In this lesson, we solved two practice problems that showed us how to apply Bayes' theorem, one of the most useful real-world formulas used to calculate probability. Given that it is rainy, there will be heavy traffic with probability$\frac{1}{2}$, and given that it is not rainy, there will be heavy traffic with probability$\frac{1}{4}$. The ball lands in the garden '24 004B 50 ft 16. You win if the 6 balls you pick match the six balls selected by the machine. Percent Word Problems Handout Revised @2009 MLC page 3 of 8 Percent Word Problems Directions: Set up a basic percent problem. Probability of choosing 2 red balls = 1 Probability of choosing 2 black balls = 3C2 = 3 Total number of possible combinations = 6C2 = 15 Probability of picking 2 balls of same colour = 4/15 Probability of picking 2 balls of different colour = 1 -. An urn contains 1 red ball and 10 blue balls. The answers and explanations are given for the practice questions. It is the ratio of the number of ways an event can occur to the number of possible outcomes. One Way No girls Boy Boy Boy. A box contains n balls coloured 1 to n. Find the probability that he is at the airport at time 3. I didn't know how extensive the site was until I bought the book. The ball so drawn is found to be red in colour. The ratio of green balls to blue balls is 1 : 2 Bag 3 contains: Red balls equal total number of green and blue balls in bag 2. A ball is chosen at random from urn 1 and put into urn 2. You can write it as a fraction - in rational form or as a percentage. Since all the w + b balls are equally likely, p = w b+w. Two balls are then drawn in succession. Compute the probability of randomly guessing the answers and getting exactly 9 questions correct. We discuss the takeaways from Michigan’s 10-3 win over Iowa, where there was a ton of positives on both sides of the ball in a defensive masterpiece by Don Brown. I'm studying probability. In this case the host can open either B or C. If the ball is red, we put two red balls back to the urn. Two balls are drawn from the urn one after the other without replacement. Odds and Evens. Object Picking Probability - Sample Math Practice Problems The math problems below can be generated by MathScore. Solved examples with detailed answer description, explanation are given and it would be easy to understand - Page 3. The hypergeometric distribution is the basic distribution of probability. The answers and explanations are given for the practice questions. and E 1 and E 2 are said to be independent events. We randomly pick a ball. One is Green, one is Black and the other two are Yellow. So the desired probability is 2/4 = 1/2. Homework Equations 3. 1 that it has failed as a short circuit. To solve dice rolling problems, you could have one dice, or you could have three dice. [Delhi 2007] Sol. 1: Solution 1 : In the event of drawing a ticket from a bag containing 100 tickets, the sample space is,. Intermediate Counting & Probability and Intermediate Counting & Probability Solutions Manual (The Art of Problem Solving) (The Art of Problem Solving) by David Patrick | Jan 1, 2007 5. What are the 4 solutions of this easy number puzzle? None of the students can have numbers 1 or 10, since they would guess the other one's number with no problems. of total outcomes Let there be a bag with 10 blue balls, 7 red balls, 16 white balls, 8 green balls and 5 purple balls. Find the probability that a ball d rawn from a bag at random is (i) Red ball (ii) blue ball 3. She will note its colour. This probability is written , notation for the probability of B given A. What probability should be assigned to the event that at least one ball has an odd number?. Use some helpful study tips so you're well-prepared to take a probability exam. Current estimates show that p= 0. The Monty Hall Problem The Monty Hall Problem gets its name from the TV game show, Let's Make A Deal, hosted by Monty Hall 1. Determine how many balls must be under that ball to make the next layer of a pyramid. There were quite a few snaps on Saturday when Jordan Jefferson played nose guard, Tykee Smith played spear and Nicktroy Fortune and Tavian. (this problem is harder than what would be on the exam, but it is a useful application of probability for those interested in genetics) Each hereditary trait in an offspring depends on a pair of genes, one contributed by the father and the other by the mother. A ball is drawn at random and is put back into the um along with k additional balls of the same colour as that of the ball drawn. From a bag containing 6 pink and 8 orange balls, 8 balls are drawn at random. n(S) is the number of elements in the sample space S and n(E) is the number of elements in the event E. 3 A die is rolled once. Problem: Solution: 1: Spin a spinner numbered 1 to 7, and toss a coin. The problem is a bit awkwardly worded. A common topic in introductory probability is problems involving a deck of standard playing cards. Whatever the problem, there’s a coach who can offer help. Three balls are drawn at random from the bag. An urn contains 1 red ball and 10 blue balls. Two balls are taken out, Let event A occur when the ﬁrst ball is red and B when the second ball is red. Blitzstein and Jessica Hwang c Chapman & Hall/CRC Press, 2014 Joseph K. Homework Equations 3. However, if you toss two coins, the probability of getting 2 heads is a compound events because once again it combines two simple events. Python Exercises, Practice, Solution: Python is a widely used high-level, general-purpose, interpreted, dynamic programming language. the probability of choosing a red ball is$\frac{30}{100}$, and we repeat this in$20. If you use the word OR then you use + in the calculation. Calculate the probability that: (i)both balls are green; (ii)the second ball is green. Suppose that this experiment is done and you learn that a white ball was selected. Bernoulli’s Principle Lesson — Bernoulli Equation Practice Worksheet Answers Bernoulli Equation Practice Worksheet Problem 1 Water is flowing in a fire hose with a velocity of 1. 20 A jar contains 3 white balls and 2 red balls. Problem : When a user draws a red ball he looses his money while if he draws a ball of some other color his money is doubled. As for the exact probability of getting a dice problem is something only privy to those over at GMAC. Probability Spinners (Basic) FREE Use the pictures of the spinners to determine the probability of outcomes for events. First case – If both ball is white – So, Concerned Event = 10 C0. Explore what probability means and why it's useful. So the probability of getting a blue is 1/3. Persons having the gene pair A, a are normal in appearance and, because they can pass on the trait to their o spring, are. 1) A student earned a grade of 80% on a math test that had 20 problems. Find the probability that both balls are the same color? b. I refer to it often as a gambler with an interest in probability and statistics, but this question actually pertains to my work. SOLVED PROBLEMS Problem 14. Let E = Event that the sum is a prime number. If the softball pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes? round to 3 decimal places. Six buses were filled and 7 students traveled in cars. What is the probability of getting an odd number on the spinner and a tail on the coin? None of the above. ; Featured Quotes — View all the quotations that have previously been featured as the Quote of the Day, in the order of their initial implication. Two balls are chosen from the jar, with replacement. These learning modules are based on the official sample problems and solutions, provided by the Society of Actuaries and Casualty Actuarial Society (that we took January 1, 2011 and used with permission). Determine the probability that both balls are red. Problems in Probability: Problems with Solutions. Problem 34. These are "real world" problems, rather than abstract riddles about sets or trigonometry etc.