question_answer 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 and girls given that (i) the youngest is a girl. (ii) At least one is a gril.  

Answer:

S = {(b, b), (b, g), (g, b), (g, g)}       where b = Boy, g = girl       (i) Let first element in each ordered pair is younger than the other.       Let E = event that both children are girls = {g, g}       And F = event that the youngest child is girl             = {(g, b), (g, g)}                   Now required conditional probability             (ii) Let x = event that both children are girls = {g, g}             any y = event that atleast one child is a girl             = {(b,g), (g, b), (g, g)}                         Now required conditional probability is