Suppose that it rains in Spain an average of once every 10 days, and when it does, hurricanes have a 8% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 7% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford? (Round your answer to four decimal places.)

The probability that it rains in Spain when hurricanes happen in Hartford is 0.1127

Step-by-step explanation:

This is a question where you use must use Bayes' Theorem.

The easiest way to do Bayes' type questions is to carefully define your terms.

Let R be the event that it is raining in Spain. R' is the event it isn't.

Let H be the event that it is hurricane in Hartford. H' is the event it isn't.

We know

P (R) = 1/10,

P (H | R) = 0.08,

P (H | R') = 0.07 and we want P (R | H).

Bayes Theorem says P (R | H) = [P (H | R) * P (R) ] / P (H)

where

P (H) = P (H | R) * P (R) + P (H | R') * P (R')

Therefore,

P (R | H) = [P (H | R) * P (R) ] / [P (H | R) * P (R) + P (H | R') * P (R') ]

P (R | H) = [0.08 * 1/10] / [ (0.08 * 1/10) + (0.07 * (1 - 1/10) ]

P (R | H) = 8 / 71

P (R | H) = 0.1127

Therefore, the probability that it rains in Spain when hurricanes happen in Hartford is 0.1127.