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- ggrree

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?

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- ggrree

- chestercat

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- ggrree

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

what are the possible outcomes?

- anonymous

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

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- ggrree

LOL

- ggrree

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

- anonymous

damned arithmetic

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