Q:

A class contain 10 men and 20 women of which half the men and half the women have brown eyes. Find the probability of P that a person chosen at random is a man or has brown eyes.

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A class contain 10 men and 20 women of which half the men and half the women have brown eyes. Find the probability of P that a person chosen at random is a man or has brown eyes.

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Let A={person is a man}  , B={person has brown eyes}
We seek P(A∪B)
P(A)=10/30=1/3    ,P(B)=15/30=1/2    
Thus P(A∪B)=P(A)+P(B)-P(A∩B)
=1/3+1/2-1/6=4/6=2/3

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