# Hypergeometric Distribution Question

• Nov 8th 2009, 03:29 AM
MATHDUDE2
Hypergeometric Distribution Question

Q: In a math class of 20 students, 5 are bilingual. If the class is randomly divided into 4 teams,

a) what is the probability that a team has fewer than 2 bilingual students?
b) what is the expected number of bilingual students on a team?

A: a) 0.6339
b) 1.25

I can't figure out how to deal with the 4 teams. Using the standard hypergeometric formula, I've come up with:
n=20
a=5
x= variable
r=4

If someone could please show me what to solve this, that would be great.

Thanks
• Nov 8th 2009, 04:16 AM
galactus
Quote:

Originally Posted by MATHDUDE2

Q: In a math class of 20 students, 5 are bilingual. If the class is randomly divided into 4 teams,

Quote:

a) what is the probability that a team has fewer than 2 bilingual students?
Don't make it too difficult.

We are choosing 5 from the 20. Of these, there are two cases, if there is 1 bilingual and when there are no bilingual.

For the 1 case, we choose 1 from the 5 binlingual and the other 4 come from the 15 non-bilingual.

$\frac{\binom{5}{1}\cdot\binom{15}{4}}{\binom{20}{5 }}$

For the 0 case, $\frac{\binom{5}{0}\cdot\binom{15}{5}}{\binom{20}{5 }}$