Question

The Boston Red Sox are going to play a 3 game series with the New York Yankees this weekend. Based on the pitching match-ups and past performances, the probability the Red Sox win each individual game is estimated as follows: (** all games are independent **) P(Red Sox win Friday's game) = 0.3 P(Red Sox win Saturday's game) = 0.9 P(Red Sox win Sunday's game) = 0.45 Based on the above probabilities, please answer the following: a.) Find the probability the Red Sox lose Friday's game. b.) Find the Probability the Red Sox win Saturday's game AND Sunday's game. c.) Find the Probability the Red Sox win all three games. d.) Find the probability the Red Sox lose all three games. e.) Find the probability the Red Sox win at least one game out of the three played.

Answer 1

a) The probability the Red Sox lose Friday's game is 0.7. b) The probability the Red Sox win Saturday's game AND Sunday's game is 0.405. c) The probability the Red Sox win all three games is 0.1215. d) The probability the Red Sox lose all three games is 0.1653. e) The probability the Red Sox win at least one game out of the three played is 0.8347.

Step-by-step explanation:

a) To find the probability that the Red Sox lose Friday's game, we subtract the probability that they win from 1. So, it is 1 - 0.3 = 0.7.

b) To find the probability that the Red Sox win Saturday's game AND Sunday's game, we multiply the probabilities of winning each game. So, it is 0.9 * 0.45 = 0.405.

c) To find the probability that the Red Sox win all three games, we multiply the probabilities of winning each game. So, it is 0.3 * 0.9 * 0.45 = 0.1215.

d) To find the probability that the Red Sox lose all three games, we multiply the probabilities of losing each game. So, it is (1 - 0.3) * (1 - 0.9) * (1 - 0.45) = 0.1653.

e) To find the probability that the Red Sox win at least one game out of the three played, we subtract the probability that they lose all three games from 1. So, it is 1 - 0.1653 = 0.8347.