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[SOLVED] Exactly k childen are boys

evinda

Well-known member
MHB Site Helper
Apr 13, 2013
3,718
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)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,684
Hey evinda !!

Yes, that is correct. (Nod)
 

evinda

Well-known member
MHB Site Helper
Apr 13, 2013
3,718

Dhamnekar Winod

Active member
Nov 17, 2018
100
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 $P(X=k)=\binom{n}{k}p^k (1-p)^{n-k}$