It rains in Spain an average of once in 10 days, and when it does, hurricanes have a 5% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 1% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford Please, round your answer to four decimal places. ?
A)0.0397
B) 0.3571
C) 0.16
D) 0.3846
E) 0.06

Question

It rains in Spain an average of once in 10 days, and when it does, hurricanes have a 5% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 1% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford  Please, round your answer to four decimal places. ?
A)0.0397
B) 0.3571
C) 0.16
D) 0.3846
E) 0.06

Quizplus · Accepted Answer

To find the probability that it rains in Spain given that a hurricane happens in Hartford, we use Bayes' theorem. Let R be the event that it rains in Spain, and H be the event of a hurricane in Hartford. We're looking for P(R|H).P(R) = 1/10 (it rains in Spain 1 out of 10 days),P(~R) = 9/10 (it does not rain in Spain 9 out of 10 days),P(H|R) = 0.05 (5% chance of hurricane if it rains),P(H|~R) = 0.01 (1% chance of hurricane if it does not rain).P(H) = P(H and R) + P(H and ~R) = P(H|R)P(R) + P(H|~R)P(~R) = (0.05)(1/10) + (0.01)(9/10) = 0.005 + 0.009 = 0.014.P(R|H) = P(H|R)P(R) / P(H) = (0.05)(1/10) / 0.014 = 0.005 / 0.014 = 0.3571.

It Rains in Spain an Average of Once in 10