A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. Theslots 0 and 00 are colored green, 18 of the others are red, and 18are black.The dealer spins the wheel and at the same time rolls asmall ball along the wheel in the opposite direction. The wheel iscarefully balanced so that the ball is equally likely to land inany slot when the wheel slows. Gamblers can bet on variouscombinations of numbers and colors. (a)If you bet on “red,” you winif the ball lands in a red slot. What is the probability of winningwith a bet on red in a single play of roulette? (b)You decide toplay roulette four times, each time betting on red. What is thedistribution of X, the number of times you win? (c)If you bet thesame amount on each play and win on exactly four of the eightplays, then you will “break even.” What is the probability that youwill break even? (d)If you win on fewer than four of the eightplays, then you will lose money. What is the probability that youwill lose money?
