What Is the Probability That Exactly 3 Out of 8 Children Are Girls?

[thegreengineer]

Right now I'm having a problem with a statistics problem. More specifically with a binomial distribution problem.

The problem says:
There is a family composed by 8 children. Calculate the probability that 3 of them are girls

As far as I know, binomial distribution formula says:
p(x=k)=\binom{n}{k}(p)^{k}(1-p)^{n-k}

In which:
*n is the number of trials
*k is the number of success
*p is the probability of success
*(1-p) is the probability of failure, sometimes denoted as q in some textbooks

I know two things, since we are talking about eight children then n=8. The number of success is k=3, therefore the number of failures must be n-k= 5. At this point I feel I'm going well. However the problem begins that problem isn't giving me the probability of success (p). I first tried to calculate it by knowing that if 8 children means 100% of all the trials then 3 girls means 37.5% (I found this by rule of three); yet I'm not completely sure if that's the right way of finding the probability of success p when problem isn't giving it to us.

Thanks.

 

[Ray Vickson]

Right now I'm having a problem with a statistics problem. More specifically with a binomial distribution problem.

The problem says:
There is a family composed by 8 children. Calculate the probability that 3 of them are girls

As far as I know, binomial distribution formula says:
p(x=k)=\binom{n}{k}(p)^{k}(1-p)^{n-k}

In which:
*n is the number of trials
*k is the number of success
*p is the probability of success
*(1-p) is the probability of failure, sometimes denoted as q in some textbooks

I know two things, since we are talking about eight children then n=8. The number of success is k=3, therefore the number of failures must be n-k= 5. At this point I feel I'm going well. However the problem begins that problem isn't giving me the probability of success (p). I first tried to calculate it by knowing that if 8 children means 100% of all the trials then 3 girls means 37.5% (I found this by rule of three); yet I'm not completely sure if that's the right way of finding the probability of success p when problem isn't giving it to us.

Thanks.

I think they want you to assume that boy and girl babies are equally likely, so that $p = q = 1/2$. In reality that is not quite true; if you want, you can look up the boy/girl birth rates in a database, and use that instead. However, assuming $p = q = 1/2$ in such problems is pretty standard in an introductory course.

 

[haruspex]

There is a family composed by 8 children. Calculate the probability that 3 of them are girls

Exactly three in total, at least three in total, or a specific three? Ok, I agree they probably mean exactly three in total.