Please give step by step explanations.

Question 44(4 points)

LetAbe the event that a flight from New York to San Francisco arrives on time and letBbe the event that it is a clear day in San Francisco. Suppose the probability of a clear day isP(B) = 0.6. We also know that the probability a plane arrives on time on a sunny day isP(A|B) = 0.9, and on a cloudy day it isP(A|B^C) = 0.5. The probability it is a cloudy day, given that the plane was late, is:

Question 44 options:

0.77.

0.5.

0.54.

0.46.