1118 CHAPTER 11 Further Topics in Algebra 69. License Plates How many different license plates can be formed with a letter followed by 3 digits and then 3 letters? How many such license plates have no repeats? 70. Racetrack Bets Most racetracks have “compound” bets on 2 or more horses. An exacta is a bet in which the first and second finishers in a race are specified in order. A quinella is a bet on the first 2 finishers in a race, with order not specified. (a) In a field of 9 horses, how many different exacta bets can be placed? (b) How many different quinella bets can be placed in a field of 9 horses? 71. Drawing a Marble A marble is drawn at random from a box containing 4 green, 5 black, and 6 white marbles. Find the following probabilities. (a) A green marble is drawn. (b) A marble that is not black is drawn. (c) A blue marble is drawn. (d) What are the odds in favor of drawing a marble that is not white? 72. Drawing a Card A card is drawn from a standard deck of 52 cards. Find the following probabilities. (a) A black king is drawn. (b) A face card or an ace is drawn. (c) An ace or a diamond is drawn. (d) A card that is not a diamond is drawn. (e) What are the odds in favor of drawing an ace? 73. Master’s Degrees The table shows the numbers of master’s degrees awarded in the United States in 2017 in several fields of study. Field of Study Number of Master’s Degrees Business 187,404 Education 145,680 Health professions and related programs 119,273 Visual and performing arts 17,523 Other 334,804 Data from National Center for Education Statistics. (a) What is the probability that a randomly selected student who earned a master’s degree in 2017 earned a degree in business? (b) What is the probability that a randomly selected student who earned a master’s degree in 2017 earned a degree in either health professions and related programs or the visual and performing arts? (c) What is the probability that a randomly selected student who earned a master’s degree in 2017 earned a degree that was not in education? 74. Defective Toaster Ovens A sample shipment of 5 toaster ovens is chosen. The probability of exactly 0, 1, 2, 3, 4, or 5 toaster ovens being defective is given in the table. Number Defective 0 1 2 3 4 5 Probability 0.31 0.25 0.18 0.12 0.08 0.06 Find the probability that the given number of toaster ovens are defective. (a) no more than 3 (b) at least 2 (c) more than 5 75. Rolling a Die A fair die is rolled 12 times. Find the probability (to three decimal places) that exactly 2 of the rolls result in a 5. 76. Tossing a Coin A fair coin is tossed 10 times. Find the probability (to three decimal places) that exactly 4 of the tosses result in a tail.
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