Suppose that it rains in Spain an average of once every 14 days, and when it doe

Question

Suppose that it rains in Spain an average of once every 14 days, and when it does, hurricanes have a 3% 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? (Round your answer to four decimal places Suppose that it rains in Spain an average of once every 14 days, and when it does, hurricanes have a 3% 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? (Round your answer to four decimal places

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Suppose that it rains in Spain an average of once every 14 days, and when it does, hurricanes have a 3% 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? (Round your answer to four decimal places)

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

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

We know P(S) = 1/14, P(H|S)=0.03, P(H|S') = 0.01;

P(S') = 13/14

we want P(S|H).

Bayes Theorem says P(S|H) = P(H|S)P(S)/P(H)

P(H) = P(H|S)P(S) + P(H|S')P(S')

=0.03*1/14+0.01*13/14

=0.01143

P(S|H) = P(H|S)P(S)/P(H)

=(0.03*1/14)/ 0.01143

=0.18748

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