Question

In a class, having 60% boys, 5% of the boys and 10% of the girls have an I.Q. of more than 150. A student is selected at random and found to have an I.Q. of more than 150. Find the probability that the selected student is a boy.

Answer 1

hope it will help you.

Answer 2

Answer:

$\frac{3}{7}$

Step-by-step explanation:

Let B = event of being a boy,

G = event of being a girl,

Q = event of having I.Q. more than 150,

Then according to the question,

P(B) = 60% = 0.60,

⇒ P(G) = 1 - P(B) = 1 - 0.60 = 0.40

P(B∩Q) = 5% of 0.60 = 0.03,

P(G∩Q) = 10% of 0.40 = 0.04,

⇒ P(Q) = P(B∩Q) + P(G∩Q) = 0.03 + 0.04 = 0.07,

Hence, if it is given that the I.Q. is more than 150 then the probability that the student is a boy,

$P(\frac{B}{Q})=\frac{P(B\cap Q)}{P(Q)}=\frac{ 0.03}{0.07}=\frac{3}{7}$