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.
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 .