MHB Probability distribution of girls

[annie122]

A certain couple is equally likely to
have either a boy or a girl. If the family has four children, let X
denote the number of girls.

Determine the probability distribution of X. (Hint: There are
16 possible equally likely outcomes. One is GBBB, meaning
the first born is a girl and the next three born are boys.)

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i don't understand why there are 16 outcomes not 5.
there can be 0, 1, 2, 3, or 4 girls..

 

[chisigma]

A certain couple is equally likely to
have either a boy or a girl. If the family has four children, let X
denote the number of girls.

Determine the probability distribution of X. (Hint: There are
16 possible equally likely outcomes. One is GBBB, meaning
the first born is a girl and the next three born are boys.)

=============

i don't understand why there are 16 outcomes not 5.
there can be 0, 1, 2, 3, or 4 girls..

The formula for probability of 'k over n' events is...

$\displaystyle P_{k,n} = \binom {n}{k} p^{k}\ (1-p)^{n - k}\ (1)$

... where $\displaystyle \binom {n}{k} = \frac{n!}{k!\ (n-k)!}$. In your case is $n=4$ and $p= \frac{1}{2}$ so that...

Kind regards

$\chi$ $\sigma$

 

[I like Serena]

i don't understand why there are 16 outcomes not 5.
there can be 0, 1, 2, 3, or 4 girls..

The problem is that those outcomes are not equally likely.

Each child can either be a boy or a girl.
Those 2 outcomes are equally likely.

If we look at only 2 children, the outcomes that are equally likely are BB, BG, GB, GG.
As you can see the outcome of 1 girl is twice as likely as 0 girls.

In the case of 4 children, what would be the probability of 0 girls?