# [SOLVED]Exactly k childen are boys

#### evinda

##### Well-known member
MHB Site Helper
Hello!!!

A couple gets $n$ children. At each birth, the probability to get a boy is $p$ (independent births). Which is the probability that exactly $k$ of the children are boys?

I have thought the following:

Let $X$ be the number of boys that the couple gets. Then the desired probality is

$P(X=k)=p^k \cdot (1-p)^{n-k}$

Am I right?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Hey evinda !!

Yes, that is correct.

MHB Site Helper

#### Dhamnekar Winod

##### Active member
Hello!!!

A couple gets $n$ children. At each birth, the probability to get a boy is $p$ (independent births). Which is the probability that exactly $k$ of the children are boys?

I have thought the following:

Let $X$ be the number of boys that the couple gets. Then the desired probality is

$P(X=k)=p^k \cdot (1-p)^{n-k}$

Am I right?
Hello,

Your answer should be $P(X=k)=\binom{n}{k}p^k (1-p)^{n-k}$