1. The probability that a fisherman catches a tuna in any one excursion is .15. What is the probability that he catches a tuna on each of three excursions? On at least one of three excursions?
2. A baseball player's batting average changes every time he goes to bat and therefore should not be used as the probability of his getting a hit. However, we can still make a subjective assessment of his ability.
(a) If a player with .3 probability of getting a hit bats four times in a game and each at-bat is an independent event, what is the probability of the player getting at least one hit in the game?
(b) What is the probability of the player in part (a) starting off the season with at least one hit in each of the first 10 games?
(c) If there are 20 players with .3 probability of getting a hit, what is the probability that at least one of them will start the season with a 10-game hitting streak?
3. If you bet on the number 7 in roulette, the probability of winning on a single spin of the wheel is 1 38. Suppose that you bet on 7 for 1/38 consecutive spins.
(a) Which of the following numbers do you think is closest to the probability of winning at least once: 1, .64, or .5?
(b) Calculate the probability of winning at least once?