elemprob-page7

# elemprob-page7 - Answer Let D be the families that own a...

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Unformatted text preview: Answer. Let D be the families that own a dog, and C the families that own a cat. We are given P ( D ) = . 36 , P ( C ) = . 30 , P ( C | D ) = . 22 We want to know P ( D | C ). We know P ( D | C ) = P ( D ∩ C ) / P ( C ). To find the numerator, we use P ( D ∩ C ) = P ( C | D ) P ( D ) = ( . 22)( . 36) = . 0792. So P ( D | C ) = . 0792 /. 3 = . 264 = 26 . 4%. Example. Suppose 30% of the women in a class received an A on the test and 25% of the men received an A. The class is 60% women. Given that a person chosen at random received an A, what is the probability this person is a women? Answer. Let A be the event of receiving an A, W be the event of being a woman, and M the event of being a man. We are given P ( A | W ) = . 30 , P ( A | M ) = . 25 , P ( W ) = . 60 and we want P ( W | A ). From the definition P ( W | A ) = P ( W ∩ A ) P ( A ) . As in the previous example, P ( W ∩ A ) = P ( A | W ) P ( W ) = ( . 30)( . 60) = . 18 ....
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