Problem 2.1P: A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking... Problem 2.2P: In an experiment, die is rolled continually until a 6 appears, at which point the experiment stops.... Problem 2.3P: Two dice are thrown. Let E be the event that the sum of the dice is odd, let F be the event that at... Problem 2.4P: A, B, and C take turns flipping a coin. The first one to get a head wins. The sample space of this... Problem 2.5P: A system is composed of 5 components, each of which is either working or failed. Consider an... Problem 2.6P: A hospital administrator codes incoming patients suffering gunshot wounds according to whether they... Problem 2.7P: Consider an experiment that consists of determining the type of job-either blue collar or white... Problem 2.8P: Suppose that A and B are mutually exclusive events for which P(A) = .3 and P(B) = .5. What is the... Problem 2.9P: A retail establishment accepts either the American Express or the VISA credit card. A total of 24... Problem 2.10P: Sixty percent of the students at a certain school wear neither a ring nor a necklace. Twenty percent... Problem 2.11P: A total of 28 percent of American males smoke cigarettes. 7 percent smoke cigars, and 5 percent... Problem 2.12P: An elementary school is offering 3 language classes: one in Spanish. one In French. and one in... Problem 2.13P: A certain town with a population of 100.000 has 3 newspapers: I, II, and Ill. The proportions of... Problem 2.14P: The following data were given in a study of a group of 1000 subscribers to a certain magazine: In... Problem 2.15P: If it is assumed that all (525) poker hands are equally likely, what is the probability of being... Problem 2.16P: Poker dice is played by simultaneously rolling 5 dice. Show that a. P{no two alike} = .0926; b.... Problem 2.17P: Twenty five people, consisting of 15 women and 10 men are lined up in a random order. Find the... Problem 2.18P: Two cards are randomly selected from an ordinary playing deck. What is the probability that they... Problem 2.19P: Two symmetric dice have had two of their sides painted red, two painted black, one painted yellow,... Problem 2.20P: Suppose that you are playing blackjack against a dealer. In a freshly shuffled deck, what is the... Problem 2.21P: A small community organization consists of 20 families, of which 4 have one child. 8 have two... Problem 2.22P: Consider the following technique for shuffling a deck of n cards: F of any initial ordering of the... Problem 2.23P: A pair of fair dice is rolled. What is the probability that the second die lands on a higher value... Problem 2.24P: It two dice are rolled, what is the probability that the sum of the upturned faces equals 1? Find it... Problem 2.25P: A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs... Problem 2.26P: The game of craps is played as follows: A player rolls two dice. If the sum of the dice is either a... Problem 2.27P: An urn contains 3 red and 7 black balls. Players A and B withdraw balls from the urn consecutively... Problem 2.28P: An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is... Problem 2.29P: An urn contains n white and m black balls, where n and m are positive numbers. a. If two balls are... Problem 2.30P: The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each... Problem 2.31P: A 3-person basketball team consists of a guard, a forward, and a center. a. If a person is chosen at... Problem 2.32P: A group of individuals containing b boys and g girls is lined up in random order: that is, each of... Problem 2.33P: A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later,... Problem 2.34P: The second Earl of Yarborough is reported to have bet at odds of 1000 to 1 that a bridge hand of 13... Problem 2.35P: Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls.... Problem 2.36P: Two cards are chosen at random from a deck of 52 playing cards. What is the probability that they a.... Problem 2.37P: An instructor gives her class a set of 10 problems with the Information that the final exam will... Problem 2.38P: There are n socks. 3 of which are red, in a drawer. What is the value of n if, when 2 of the socks... Problem 2.39P: There are 5 hotels in a certain town. If 3 people check into hotels in a day, what is the... Problem 2.40P: If 4 balls are randomly chosen from an urn containing 4 red, 5 white, 6 blue, and 7 green balls,... Problem 2.41P: If a die is rolled 4 times, what is the probability that 6 comes up at least once? Problem 2.42P: Two dice are thrown n times in succession. Compute the probability that double 6 appears at least... Problem 2.43P: a. If N people, including A and B, are randomly arranged in a line, what is the probability that A... Problem 2.44P: Five people, designated as A, B, C, D, E, are arranged in linear order. Assuming that each possible... Problem 2.45P: A woman has n keys, of which one will open her door. a. If she tries the keys at random, discarding... Problem 2.46P: How many people have to be in a room in order that the probability that at least two of them... Problem 2.47P: Suppose that 5 of the numbers 1, 2,..., 14 are chosen. Find the probability that 9 is the third... Problem 2.48P: Given 20 people, what is the probability that among the 12 months in the year, there are 4 months... Problem 2.49P: A group of 6 men and 6 women is randomly divided into 2 groups of size 6 each. What is the... Problem 2.50P: In a hand of bridge, find the probability that you have 5 spades and your partner has the remaining... Problem 2.51P: Suppose that n balls are randomly distributed into N compartments. Find the probability that m balls... Problem 2.52P: A closet contains 10 pairs of shoes. If 8 shoes are randomly selected, what is the probability that... Problem 2.53P: If 8 people, consisting of 4 couples, are randomly arranged In a row, find the probability that no... Problem 2.54P: Compute the probability that a bridge hand is void in at least one suit. Note that the answer is not... Problem 2.55P: Compute the probability that a hand of 13 cards contains a. the ace and king of at least one suit:... Problem 2.56P: Two players play the following game: Player A chooses one of the three spinners pictured in Figure... Problem 2.1TE: Prove the following relations: EFEEF Problem 2.2TE: Prove the following relations: If EF, then FCEC. Problem 2.3TE: Prove the following relations: 3. F=FEFEC and EF=EECF , Problem 2.4TE: Prove the following relations: (1Ei)F=1EiF and (1Ei)F=1(EiF). Problem 2.5TE: For any sequence of events E1,E2,..., define a new sequence F1,F2,... of disjoint events (that is.... Problem 2.6TE: Let E, F, and C be three events. Find expressions for the events so that. of E, F, and C, a. only E... Problem 2.7TE: Use Venn diagrams a. to simplify the expression (EF)(EFC); b. to prove DeMorgans laws for events E... Problem 2.8TE Problem 2.9TE: Suppose that an experiment is performed n times For any event E of the sample space. let n(E) denote... Problem 2.10TE: Prove thatP(EFC)=P(E)+P(F)+P(C)P(ECFG)P(EFCG)P(EFGC)P(EFGC)2P(EFC). Problem 2.11TE: If P(E)=.9 and P(F)=.8, show that P(EF).7. In general, prove Bonferronis inequality,... Problem 2.12TE: Show that the probability that exactly one of the events E or F occurs equalsP(E)+P(F)2P(EF). Problem 2.13TE: Prove that P(EF)=P(E)P(EF). Problem 2.14TE: Prove Proposition 4.4 by mathematical induction. Problem 2.15TE: An urn contains M white and N black balls. If a random sample of size r is chosen, what is the... Problem 2.16TE: Use induction to generalize Bonferronis inequality to n events. That is. show... Problem 2.17TE: Consider the matching problem. Example 5m, and define AN to be the number of ways in which the N men... Problem 2.18TE: Let fn, denote the number of ways of tossing a coin n times such that successive heads never appear.... Problem 2.19TE: An urn contains n red and m blue balls. They are withdrawn one at a time until a total of r, rn red... Problem 2.20TE: Consider an experiment whose sample space consists of a countably infinite number of points. Show... Problem 2.21TE: Consider Example 50, which is concerned with the number of runs of wins obtained when n wins and m... Problem 2.1STPE: A cafeteria offers a three-course meal consisting of an entree. a starch, and a dessert. The... Problem 2.2STPE: A customer visiting the suit department of a certain store will purchase a suit with probability... Problem 2.3STPE: A deck of cards is dealt out. What is the probability that the 14th card dealt is an ace? What is... Problem 2.4STPE: Let A denote the event that the midtown temperature in Los Angeles is 70F, and let B denote the... Problem 2.5STPE: An ordinary deck of 52 cards is shuffled. What is the probability that the top four cards have a.... Problem 2.6STPE: Urn A contains 3 red and 3 black balls, whereas urn B contains 4 red and 6 black balls. If a ball is... Problem 2.7STPE: In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then... Problem 2.8STPE: From a group of 3 first-year students, 4 sophomores, 4 juniors, and 3 seniors, a committee of size 4... Problem 2.9STPE: For a finite set A, let N(A) denote the number of elements in A. a. Show that N(AB)=N(A)+N(B)N(AB)... Problem 2.10STPE: Consider an experiment that consists of 6 horses, numbered 1 through 6, running a race, and suppose... Problem 2.11STPE: A 5-card hand is dealt from a well-shuffled deck of 52 playing cards. What is the probability that... Problem 2.12STPE: A basketball team consists of 6 frontcourt and 4 backcourt players. If players are divided into... Problem 2.13STPE: Suppose that a person chooses a letter at random from R E S E R V E and then chooses one at random... Problem 2.14STPE: Prove Booles inequality P(i=1Ai)i=1P(Ai) Problem 2.15STPE: Show that if P(Ai)=1 for all i1, then P(i=1Ai)=1. Problem 2.16STPE: Let Tk(n) denote the number of partitions of the set {1,...,n} into k nonempty subsets, where 1kn.... Problem 2.17STPE: Five balls are randomly chosen, without replacement, from an urn that contains 5 red, 6 white, and 7... Problem 2.18STPE: Four red, 8 blue, and 5 green balls are randomly arranged in a line. a. What is the probability that... Problem 2.19STPE: Ten cards are randomly chosen from a deck of 52 cards that consists of 13 cards of each of 4... Problem 2.20STPE: Balls are randomly removed from an urn initially containing 20 red and 10 blue balls. What is the... format_list_bulleted