Ex 13.1, 12 Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (ii) at least one is a girl? S = {(g, g), (g, b), (b, g), (b, b)}
We need to find the probability that the children are girls, given that at least one is a girl.
E : both the children are girls
F : at least one child is a girl
E = {(g, g)}
P(E) = 1/4
F = {(g, g), (g, b), (b, g)}
P(F) = 3/4
Also,
E ∩ F = {(g, g)}
So, P(E ∩ F) = 1/4
Now,
P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹))
= (1/4)/(3/4)
= 1/4 × 4/3
= 𝟏/𝟑
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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