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(U1) = 0.6
⇒ P(U2) = 0.4
⇒ P(A|U1) = P(Boy whose IQ is more than 150)
⇒ P(A|U1) = 0.05
⇒ P(A|U2) = P(Girl whose IQ is more than 150)
⇒ P(A|U2) = 0.1
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 \(\cfrac37\).