Question

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 (i) the youngest is a girl, (ii) at least one is a girl?

Answer 1

(i) 1/2
(ii) 3/4
hope it helped......

Answer 2

Answer:

= $\frac{1}{3}$

Step-by-step explanation:

A family has 2 children,

then sample space S = [ BB , BG , GB , GG ] where B stands for boy anf G stands for Girl.

  (1) Let A and B be two events such that

  A = Both for girls = [ GG ]

  B = The youngest is a girl = [ BG , GB ]

 P $(\frac{A}{B} )$ = P ( A ∩ B ) / P (B)             [ ∵ A ∩ B = { GG } ]

P (A/B) = 1/4 / 2/4 = 1/2

(2) Let C be events such that

C = at least one is a girl = [ BG , GB , GG ]

Now,  P ( A / C ) = P ( A ∩ C ) / P(C)                [ ∵ A ∩∩C = { GG } ]

     = 1/4 / 3/4

      = $\frac{1}{3}$

GOOD LUCK !!