21. In each of a set of games, it is 2 to 1 in favour of the winner of the previous game; what is the chance that the player who wins the first game shall win at least three of the next four gam:es. (K.U.B. Com., April 1999)
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- Michelle and Kim are playing a tennis match. The winner will be the first person to win two sets. Kim is the better player, and in fact whenever they play a set the probability is 2/3 that Kim will win the set. (Hint: Draw a tree diagram for a three set match) a) what is the probability that Michelle will win the match? b) if she wins the first set, what then is the probability that she will win the match? c) what is the probability that she wins the first set given that she wins the match? d) what is the probability that the match will last for three sets?6. A pizza contains three toppings randomly selected from the following choices: pepperoni, mushrooms, green peppers, ham, bacon, and onions. Manuel enjoys all toppings, except bacon and onions. What is the likelihood that a pizza will contain a) no toppings that Manuel dislikes? b) exactly one topping that Manuel dislikes? c) at least one topping that Manuel dislikes?2.10 Guessing on an exam: In a multiple choice exam, there are 4 questions and 4 choices for each question (a, b, c, d). Nạncy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (please round all answers to four decimal places) a) the first question she gets right is question number 3? b) she gets all of the questions right? c) she gets at least one question right?
- 2.2 3) For each situation below, determine whether the two events are dependent or independent. a) Flip a coin and then draw a card from a standard deck of 52 cards. b) Draw a marble from a bag; do not replace it; and then draw a 2nd marblę from the same bag. c) Get a raise at work and purchase a new car. d) Drive on ice and lose control of your car. e) Have a large shoe size and have a high IQ. f) Be a chain smoker and get lung cancer. g) Dad is left handed and son is left handed INTL 9 DII -> & %23 24 6. 4 2 y e6.) A mathematics class has 16 engineers majors, 12 science majors, and 4 liberal artsmajors.a.) What is the probability that a student selected at random will be a science orliberal arts major?b.) What is the probability that a student selected at random will be anengineering or science major?c.) 5 of the engineering students, 6 or the science majors, and 2 of the liberal artsmajors are female. What is the probability that a student selected at random is anengineering major or a female?a). A girl is randomly picking flowers in a meadow for a bouquet. She will stop once she has picked 4 dandelions. Suppose that a randomly selected flower is a dandelion with probability 0.70. Find the probability that her bouquet will have exactly 8 flowers in total. b). An entomologist has a collection of 20 insect specimens: 5 are butterflies and 15 are moths. He randomly selects a sample of 6 specimens to study. Find the probability that the sample contains an equal number of butterflies and moths. 2
- 7. On 25 October 2003, at the Santa Anita Racetrack in Arcadia, California, Mr. Graham Stone, from Rapid City, South Dakota, won a single bet in which he had picked the winner of six successive races! Mr. Stone had never visited a racetrack; racing fans across the nation were stunned. The winning horses, and the odds of each horse winning, as determined just before the race in which it ran, were as follows: Winning Horse Ods 1. Six Perfections 5-1 2. Cajun Beat 3. Islington 4. Action This Day 5. High Chaparral 6. Pleasantly Perfect 22–1 3-1 26-1 5-1 14-1 Mr. Stone's wager cost $8; his payoff was $2,687,661.60. The odds against such good fortune (or handicapping skill?), we might say in casual conversation, are "a million to one." Mr. Stone's payoff was at a rate far below that. Did he deserve a million-to-one payoff? How would you justify your answer?1. From a deck of 52 cards (Ace, 2, 3.......10, Jack, Queen, King; with each one havingclubs or flower, spade, heart and diamond). When a card is drawn, what is theprobability that the card is a(a) 7 (b) 7 of heart (c) heart (d) either 7 or heart2. What is the probability of getting a 2 or a 5 when a dice is rolled?3. Referring to the important health practices advocated by the California study, supposethat in a senior college class of 500 students its is found that 210 smoke, 258 drink alcoholicbeverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eatbetween meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52engage in all three of these bad health practices. If a member of this sneer class is selectedat random, find the probability that the studenta. smoke but does not drink alcoholic beverages;b. eats between meals and drinks alcoholic beverages but does not smoke;c. neither smokes nor eats between meals.30. In the faculty parking lot, – of the vehicles are cars and the rest are trucks. Four sevenths of the trucks have bumper 3 stickers on them, while only one fifth of the cars have bumper stickers. If a vehicle from this lot is chosen at random, what is the probability that it a) does not have a bumper sticker given it is a car? b) is a car without a bumper sticker? c) has a bumper sticker?
- 1what are the chances that the runn ers from Detroit and Kiercrest will finish Ist and 2nd, regardless of the acler? Thae ae a runners in the finals of the district 100 mekr race. TThree of the FrUnners are from Clarksulle, two and from Linden- Kildare, oneis from Delvait, one is from hiverenest and two are rom Naud What are the Chances that the winner of the race will vbe fream Clarksuille a lik24.) Find the probability of getting the following 5-card poker hands. (a) A royal flush (A, K, Q, J, 10 of a single suit.) (b) A straight (5 cards in a row, not all of the same suit, with ace either high or low) c) Three of a kind (exactly 3 cards of the same kind) (d) Exactly 2 different suits2. A student majoring in phycology is trying to decide on the number of firms to which he should apply. Given his work experience and grades he can expect to receive a job offer from 75% of the firms he applies. The student decides to apply to only 4 firms. What is the probability that he receives?a) No job offers P(x = 0) b) Less than 2 job offers P(x <2) c) At least 2 job offers P(x ≥ 2)
