Re:Shortest bit sequence that's never been sent over the Int...
by DavidSJ on Thursday April 19, 2018 @06:35AM
(#16874726)
Your neighbours has two children, one of which is a girl.
What is the probability of the other child to be a girl?
This is oft-mentioned but with this wording it's ambiguous. Here are three possible interpretations:
1. Your neighbor has two children. We observed both and found that there was exactly one girl. What is the probability that both are girls? (Answer: 0)
2. Your neighbor has two children. We observed one and found that she was a girl. What is the probability that the other (unobserved) child is a girl? (Answer: 1/2)
3. Your neighbor has two children. We observed both and found that there was at least one girl. What is the probability that both are girls? (Answer: 1/3)
Interpretation #1 is kind of silly but it serves to illustrate the ambiguity of the plain English wording. Interpretation #2 is how most people interpret the problem, and it's bolstered by the use of the word "other" in your prompt. For there to be an "other" child, there must have been a specific girl observed originally, rather than a general observation that there was at least one girl. Interpretation #3 is how you intended the problem.
1. Your neighbor has two children. We observed both and found that there was exactly one girl. What is the probability that both are girls? (Answer: 0)
2. Your neighbor has two children. We observed one and found that she was a girl. What is the probability that the other (unobserved) child is a girl? (Answer: 1/2)
3. Your neighbor has two children. We observed both and found that there was at least one girl. What is the probability that both are girls? (Answer: 1/3)
Interpretation #1 is kind of silly but it serves to illustrate the ambiguity of the plain English wording. Interpretation #2 is how most people interpret the problem, and it's bolstered by the use of the word "other" in your prompt. For there to be an "other" child, there must have been a specific girl observed originally, rather than a general observation that there was at least one girl. Interpretation #3 is how you intended the problem.