2.30. Consider the situation described in Example 2.24 on p. 22, but this time let us define the sample space clearly. Suppose that one child is older, and the other is younger, their gender is independent of their age, and the child you meet is one or the other with probabilities 1/2 and 1/2. (a) List all the outcomes in this sample space. Each outcome should tell the children’s gender, which child is older, and which child you have met. (b) Show that unconditional probabilities of outcomes BB, BG, and GB are equal. (c) Show that conditional probabilities of BB, BG, and GB, after you met Leo, are not equal. (d) Show that the conditional probability that Leo has a brother is 1/2.

2.30. Consider the situation described in Example 2.24 on p. 22, but this time let us define the
sample space clearly. Suppose that one child is older, and the other is younger, their gender
is independent of their age, and the child you meet is one or the other with probabilities
1/2 and 1/2.
(a) List all the outcomes in this sample space. Each outcome should tell the children’s
gender, which child is older, and which child you have met.
(b) Show that unconditional probabilities of outcomes BB, BG, and GB are equal.
(c) Show that conditional probabilities of BB, BG, and GB, after you met Leo, are not
equal.
(d) Show that the conditional probability that Leo has a brother is 1/2.