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Chapter 5: Q 41. (page 309)
Role-playing games Refer to Exercise 39. Define event A: sum is . Find .
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An unenlightened gambler
(a) A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and bets
heavily on black at the next spin. Asked why he explains that black is 鈥渄ue by the law of averages.鈥� Explain to the gambler what is wrong with this reasoning.
(b) After hearing you explain why red and black are still equally likely after five reds on the roulette wheel, the gambler moves to a poker game. He is dealt five straight red cards. He remembers what you said and assumes that the next card dealt in the same hand is equally likely to be red or black. Is the gambler right or wrong, and why?
Winning at tennis A player serving in tennis has two chances to get a serve into play. If the first serve goes out of bounds, the player serves again. If the second serve is also out, the player loses the point. Here are probabilities based on four years of the Wimbledon Championship:18 P(1st serve in) = P(win point | 1st serve in) = P(2nd serve in | 1st serve out) = P(win point | 1st serve out and 2nd serve in) =
(a) Make a tree diagram for the results of the two serves and the outcome (win or lose) of the point.
(b) What is the probability that the serving player wins the point? Show your work.
Fill 鈥檈rr up! In a recent month, of automobile drivers filled their vehicles with regular gasoline, purchased midgrade gas, and bought premium gas. Of those who bought regular gas, paid with a credit card; of customers who bought midgrade and premium gas, and , respectively, paid with a credit card. Suppose we select a customer at random.
Draw a tree diagram to represent this situation. What鈥檚 the probability that the customer paid with a credit card? Use the four-step process to guide your work.
In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of
people it contains. Here is the assignment of probabilities for your outcome:
The probability of finding people in a household is the same as the probability of finding people. These probabilities are marked ??? in the table of the distribution. The probability that a household contains 3 people must be
(a) (b) (c) (d) (e) between and, and we can say no more. 
In a table of random digits such as Table D, each digit is equally likely to be any of or What is the probability that a digit in the
table is or greater? (a) (c) (e) (b) (d)
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