Let A be the event that a flight from New York to San Francisco arrives on time and let B be the event that it is a clear day in San Francisco. Suppose the probability of a clear day is P(B) = 0.6 and the probability a plane arrives on time is P(A) = 0.7. We also know that the probability a plane arrives on time on a cloudy day is P(A | B^C) = 0.5. The probability a plane arrives on time and it is a cloudy day is: A)0.6. B)0.5. C)0.2. D)0.42.

Question

Quizplus · Accepted Answer

Using the formula for conditional probability, we have P(A | B) = P(A and B) / P(B). Solving for P(A and B), we get P(A and B) = P(A | B) * P(B) = 0.7 * 0.6 = 0.42. Therefore, the probability a plane arrives on time and it is a cloudy day is 0.42.

Let a Be the Event That a Flight from New