Ask Question
1 January, 01:08

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.)

+1
Answers (1)
  1. 1 January, 01:32
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “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. ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers