Use Bayes' theorem to find the indicated probability.
-Shameel has a flight to catch on Monday morning. His father will give him a ride to the airport. If it rains, the traffic will be bad and the probability that he will miss his flight is 0.05. If it doesn't rain, the probability that he
Will miss his flight is 0.02. The probability that it will rain on Monday is 0.30.
Suppose that Shameel misses his flight. What is the probability that it was raining?
A) 0.517
B) 0.483
C) 0.05
D) 0.30

Question

Quizplus · Accepted Answer

Using Bayes' theorem, P(Rain | Miss) = [P(Miss | Rain) * P(Rain)] / P(Miss). P(Miss) = P(Miss | Rain) * P(Rain) + P(Miss | No Rain) * P(No Rain) = 0.05 * 0.30 + 0.02 * 0.70 = 0.015 + 0.014 = 0.029. Thus, P(Rain | Miss) = (0.05 * 0.30) / 0.029 = 0.015 / 0.029 ≈ 0.517.

Use Bayes' Theorem to Find the Indicated Probability