# Math Help - Simple Probability Problem

1. ## Simple Probability Problem

I have a simple probability problem I can't get for the life of me must be over thinking it.

It is said that 40% of students drink coffee in the morning before class. If a group of 25 students were polled, what is the probability of 15 of them drinking coffee?

Any help would be appreciated thanks

2. Originally Posted by action259
I have a simple probability problem I can't get for the life of me must be over thinking it.

It is said that 40% of students drink coffee in the morning before class. If a group of 25 students were polled, what is the probability of 15 of them drinking coffee?

Any help would be appreciated thanks
I think this involves Binomial distribution. have you ever heard of it?

3. Originally Posted by action259
I have a simple probability problem I can't get for the life of me must be over thinking it.

It is said that 40% of students drink coffee in the morning before class. If a group of 25 students were polled, what is the probability of 15 of them drinking coffee?

Any help would be appreciated thanks
$P(drinks$ $coffee)= 40$% $= 2/5$ right...

We have $n= 25$ students in total...

Define a success as "A student drinks coffee."

Then,

number of students that drink coffee $= \{$ the number successes with $P(success)= 2/5\}$ ~ $Binomial(n=25,p=2/5).$

Also, we know the probability mass function is:

$P(X=k)= {n\choose k}(p)^n (1-p)^{n-k}.$ Therefore,

$P(X=15)= {25\choose 15}(2/5)^{25} (1-2/5)^{25-15}.$ Now throw that in your calculator.

4. Ok that makes sense Thanks