Answer:
The <em>probability </em>that it rains in Spain when hurricanes happen in Hartford is <em>0.1127</em>
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
<em>P(R) = 1/10, </em>
<em>P(H | R) = 0.08, </em>
<em>P(H | R') = 0.07</em> and we want <em>P(R | H)</em>.
<em>Bayes Theorem says P(R | H) = [P(H | R)×P(R)] / P(H)
</em>
<em>
where</em>
<em>P(H) = P(H | R)×P(R) + P(H | R')×P(R') </em>
<em />
Therefore,
<em>P(R | H) = [P(H | R)×P(R)] / [P(H | R)×P(R) + P(H | R')×P(R')]</em>
<em>P(R | H) = [0.08 × 1/10] / [(0.08 × 1/10) + (0.07 × (1 - 1/10)]</em>
<em>P(R | H) = 8 / 71</em>
<em>P(R | H) = 0.1127</em>
<em></em>
Therefore, the <em>probability </em>that it rains in Spain when hurricanes happen in Hartford is <em>0.1127.</em>
, where c is the hypotenuse (the longest side, in this case 53).