MHB What Is the Probability of Having Exactly k Boys in a Family of n Children?

[evinda]

Hello! (Wave)

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? (Thinking)

 

[I like Serena]

Hey evinda!

Yes, that is correct. (Nod)

 

[evinda]

Hey evinda!

Yes, that is correct. (Nod)

Great! Thank you (Happy)

 

[WMDhamnekar]

Hello! (Wave)

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? (Thinking)

Hello,

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