Just a question which i would like someone to confirm for me

for #a. i got 1/8 and #b. is larger (but i have no explination)

hopefully someone can kindly help me out

<3

4) Your new neighbour moved in recently. The family consisted of the mom, the dad, and 3 kids. You knew there were 3 kids because you could always hear 3 kids’ voices through the building’s thin wall, but you didn’t know their gender because all 3 kids were still very young, in elementary school. You’ve seen the mom and dad. They look very much alike! So you expect the kids to look relatively alike as well.

a) Out of curiosity one day you decided to see how many boys and girls (not counting the parents) were in the family, so you went to knock on their door. And 1 boy came out. What is the probability that all 3 kids are boys given that 1 came out?

As you already know the first child's gender, the options left to you for the other two kids are B-B, B-G, G-B, G-G, with B = boy, G - girl, hen is 1 out of4 or probability = $\displaystyle 0.25$

Nemesis

b) Of course you still didn’t have enough information to decide on all the 3’s gender, so you found some other excuse to knock on their door. A boy came out, but you couldn’t be sure if it was the same as the previous one or a different boy. Is the “probability that all 3 kids are boys” larger or smaller than part a)’s answer? Please explain your reasoning in a few sentences.
Thanks you in advance !