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 0.01.The probability that it will rain on Monday is 0.28.Suppose that Shameel misses his flight.What is the probability that it was raining?

A) 0.660
B) 0.340
C) 1.944
D) 0.05
E) 0.28

Question

Grace Smith · Accepted Answer

Final Answer : A, Explanation :  0.660To find the probability that it was raining given that Shameel misses his flight, we use Bayes' theorem. Let R be the event that it rains, and M be the event that Shameel misses his flight. We want to find P(R|M), the probability it was raining given that he missed his flight.P(R|M) = [P(M|R) * P(R)] / [P(M|R) * P(R) + P(M|~R) * P(~R)]Given:- P(M|R) = 0.05 (probability he misses the flight if it rains)- P(R) = 0.28 (probability it rains)- P(M|~R) = 0.01 (probability he misses the flight if it doesn't rain)- P(~R) = 1 - P(R) = 0.72 (probability it doesn't rain)Plugging in the values:P(R|M) = [0.05 * 0.28] / [(0.05 * 0.28) + (0.01 * 0.72)]       = 0.014 / (0.014 + 0.0072)       = 0.014 / 0.0212       = 0.660 (approximately)Therefore, the probability that it was raining given that Shameel misses his flight is approximately 0.660.

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