this should be an easy problem, but I can't work out the right answer for the life of me:

A couple decides to have children until they get a girl, but agree that they will not have more than 3 children, even if they are all boys. (assume boys and girls are equally likely)
What is a the probability of each outcome?
What is the expected number of children?
What is the expected number of boys?
What is the standard deviation of the number of kids?

Question

this should be an easy problem, but I can't work out the right answer for the life of me:

A couple decides to have children until they get a girl, but agree that they will not have more than 3 children, even if they are all boys.  (assume boys and girls are equally likely)
What is a the probability of each outcome?
What is the expected number of children?
What is the expected number of boys?
What is the standard deviation of the number of kids?

ggrree · Answer

from what I understand, the possible outcomes are:
1 girl: (1/2) , 1 boy and then 1 girl (1/2 * 1/2), 2 boys and 1 girl (1/6) or 3 boys (1/6).

Clearly something is wrong here because those probabilities do not add up to 1, what am I missing?

anonymous · Answer

what are the possible outcomes?

anonymous · Answer

oh i see your mistake 
$$\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{8}$$

ggrree · Answer

LOL

ggrree · Answer

THANKS! I thought 1/2 * 1/2 * 1/2 was 1/6... wow.

anonymous · Answer

damned arithmetic