(i) To Find: Write the sample space for the given experiment.
Explanation: Here, The family has 2 children
Let us Assume Boy = B
Let us Assume Girl = G
So, The number of sample spaces for 2 children is 22=4
Sample space are, S={(B1, B2), (G1, G2), (G1, B2), (B1, G2)}
Where , number 1 and 2 are represent elder and younger.
Hence, S is the sample space for given experiment.
(ii) Explanation: Here, The family has 2 children, So the possibility of boys in a family is:
(a) No boys only girl
(b) One boy and one girl
(c) Two boys only
So, The Sample space for the given condition is:
S={0, 1, 2}
Hence, S is the sample spaces for the given experiment.