Q. 95.0( 1 Vote )

In a class 5% of the boys and 10% of the girls have an IQ of more than 150. In this class, 60% of the students are boys. If a student is selected at random and found to have an IQ of more than 150, find the probability that the student is a boy.

Answer :

Let us assume U1, U2 and A be the events as follows:


U1 = choosing boy


U2 = choosing girl


A = choosing a student with IQ more than 150


From the problem:




P(A|U1) = P(Boy whose IQ is more than 150)



P(A|U2) = P(Girl whose IQ is more than 150)



Now we find


P(U1|A) = P(The choosen student whose IQ is more than 150 is a boy)


Using Baye’s theorem:







The required probabilities is .


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