Russt Wrote:Scenario 1: The younger child is named Nathan (50%)
- 25% chance that the older child is a boy
- 25% chance that the older child is a girl
Scenario 2: The older child is named Nathan (50%)
- 25% chance that the younger child is a boy
- 25% chance that the younger child is a girl
50%.
Yes, but assuming 50% of each, these are wrong.
They're not going to name both kids Nathan (well, let's hope) - so the options are these:
Girl/Girl (eliminated)
Boy/Girl (Older child named Nathan)
Girl/Boy (Younger child named Nathan)
Boy/Boy (One child named Nathan)
These 4 scenarios happen with equal likelihood, so the remaining ones all have 1 in 3 chance of happening now that one is gone (due to knowledge that at least one is a boy)
If we assume it's a 50% chance the older or younger child is named Nathan, that means:
- 1/3 + 1/6 the older child is Nathan = 50%
- 1/3 + 1/6 the younger child is Nathan = 50%
That's 1/3 (other child is a girl) + 1/6 (other child is a boy)
Total: 2/3 of the time, the other kid is a girl.
@ClawofBeta, the problem is not that the events are independent, it's that the information given is ambiguous about which event happened.