1. ## Probability

A family has eleven children. The probability of having a girl is 1/2. What is the probability of having no more than 1 boy?

2. First off I think a mod should move this since I don't think this is the right place for this topic.

So let P(x)= probability of having x boys.
Then you want $\displaystyle P(0)+P(1)$
$\displaystyle P(0) = \left(\frac{1}{2}\right)^{11}$ since there are no boys.
$\displaystyle P(1)={11\choose 1}\left(\frac{1}{2}\right)^{11}$ there are $\displaystyle {11\choose 1}$ ways to have one boy out of a group of 11 people.

3. So, if the question was like "A family has five children. The probability of having a girl is 1/2. What is the probability of having no more than 3 boys?"

Is this how you would do that?

$\displaystyle P(0) = \left(\frac{1}{2}\right)^{5}$
$\displaystyle P(1) = {5\choose 1}\left(\frac{1}{2}\right)^{5}$
$\displaystyle P(2) = {5\choose 2}\left(\frac{1}{2}\right)^{5}$
$\displaystyle P(3) = {5\choose 3}\left(\frac{1}{2}\right)^{5}$

4. Yes, that's correct.