Question

One family is selected from the families having two children. The sex (male or female) of the children from this family is noted. State the sample space of this experiment and write the sets showing the following events:

(1) Event A₁ = One child is a female
(2) Event A₂ = At least one child is a female

Answer 1

Here, let B = child is male;

G = child is female.

The sample space of selecting one family from the families having

two children is expressed as follows:
U = {(B, B), (B, G), (G, B), (G, G)}

(1) Event A₁ = One child is a female

= {(B, G), (G, B)}

(2) Event A₂ = At least one child is a female

= {(B, G), (G, B), (G, G)}