Question

Probabilities are sensitive to the form of the question that was used to generate the answer...

Probabilities are sensitive to the form of the question that was used to generate the answer

(Source: Minka.) My neighbor has two children. Assuming that the gender of a child is like a coin flip, it is most likely, a priori, that my neighbor has one boy and one girl, with probability 1/2. The other possibilities—two boys or two girls—have probabilities 1/4 and 1/4.

a. Suppose I ask him whether he has any boys, and he says yes. What is the probability that one child is a girl?

b. Suppose instead that I happen to see one of his children run by, and it is a boy. What is the probability that the other child is a girl?

Homework Answers

Answer #1

Answer:-

Given That:-

My neighbor has two children. Assuming that the gender of a child is like a coin flip, it is most likely, a priori, that my neighbor has one boy and one girl, with probability 1/2. The other possibilities—two boys or two girls—have probabilities 1/4 and 1/4.

a. Suppose I ask him whether he has any boys, and he says yes. What is the probability that one child is a girl?

a) P(one child is girl |at least one boy) =P(both girl and boy) /P(At least one boy) =(1/2)/(3/4) =2/3

b. Suppose instead that I happen to see one of his children run by, and it is a boy. What is the probability that the other child is a girl?

b) Due to independence:

P(other is a girl| given 1 is boy) =P(other is girl)=1/2


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