This season, the probability that the Yankees will win a game is 0.52 and the probability that the Yankees will score 5 or more runs in a game is 0.56 . The probability that the Yankees win and score 5 or more runs is 0.4 . What is the probability that the Yankees would score fewer than 5 runs when they lose the game? Round your answer to the nearest thousandth. Answer:

Question

Bytelearn · Accepted Answer

Define Events: Let's denote the events as follows: W: The Yankees win a game. S: The Yankees score 5 or more runs in a game. We are given the following probabilities: P(W) = 0.52 P(S) = 0.56 P(W and S) = 0.4 We need to find the probability that the Yankees score fewer than 5 runs when they lose, which can be denoted as P(S' | W'), where S' is the complement of S (scoring fewer than 5 runs) and W' is the complement of W (losing the game).Calculate Probabilities: First, we need to find the probability that the Yankees lose a game, which is the complement of the probability that they win. This can be calculated as: P(W') = 1 - P(W) P(W') = 1 - 0.52 P(W') = 0.48Find Probability of Losing and Scoring Fewer Runs: Next, we need to find the probability that the Yankees score fewer than 5 runs, which is the complement of the probability that they score 5 or more runs. This can be calculated as: P(S') = 1 - P(S) P(S') = 1 - 0.56 P(S') = 0.44Calculate Conditional Probability: Now, we need to find the probability that the Yankees lose and score fewer than 5 runs, which is P(W' and S'). We can use the complement of the probability that they win and score 5 or more runs to find this. This can be calculated as: P(W' and S') = P(S') - P(W and S) P(W' and S') = 0.44 - 0.4 P(W' and S') = 0.04Finally, we can find the probability that the Yankees score fewer than 5 runs given that they lose the game using the conditional probability formula: P(S' | W') = P(W' and S') / P(W') P(S' | W') = 0.04 / 0.48 P(S' | W') ≈ 0.0833 (rounded to the nearest thousandth)

Full solution

More problems from Find probabilities using the addition rule

Related topics