Question

One family is randomly selected from the families having two children. Find the probability that

(1) One child is a girl and one child is a boy.
(2) At least one child is a girl among the two children of the selected family.

(Note: Assume that the chance of the child being a boy or girl is same.)

Answer 1

We take, B = Boy, G = Girl

∴ The sample space for the families having two children is expressed as follows:

U = {BB, BG, GB, GG}

Now, the total number of primary outcomes of the sample space of selecting a family at random is n = ⁴C₁ = 4.

(1) A = Event that one child is a girl and one child is a boy. = {BG, GB}

∴ Favourable outcomes for the event A is m = 2.

Hence, P(A) = \(\frac{m}{n} = \frac{2}{4} = \frac{1}{2}\)

(2) B = Event that at least one child is a girl among two children of the selected family.
= {GB, BG, GG}

∴ Favourable outcomes for the event B is m = 3.

Hence, P(B) = \(\frac{m}{n} = \frac{3}{4}\)