Betting on red, continued. You decide to play roulette 200 times, each time betting the same amount on red. You will lose money if you win on fewer than 100 of the plays. Based on the information in Exercise 13.26, what is the probability that you will lose money? (Check that the Normal approximation is permissible, and use it to find this probability. If your software allows, find the exact binomial probability and compare the two results.) In general, if you bet the same amount on red every time, you will lose money if you win on fewer than half of the plays. What do you think happens to the probability of making money the longer you continue to play?

Exercise 13.26

Betting on red. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black. The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors.

(a) If you bet on “red,” you win if the ball lands in a red slot. What is the probability of winning with a bet on red in a single play of roulette?

(b) You decide to play roulette 4 times, each time betting on red. What is the distribution of X, the number of times you win?

(c) If you bet the same amount on each play and win on exactly 2 of the 4 plays, you will “break even.” What is the probability that you will break even?

(d) If you win on fewer than 2 of the 4 plays, you will lose money. What is the probability that you will lose money?

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Status NEW Posted 02 Aug 2017 01:08 PM My Price 5.00

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