Thread: probability help

A committee of size 10 is selected at random from 14 professional people and 8 are non-professional people. what is the probability that;

a) Exactly 6 members of the committee are professional people?
b) No more than 3 members of the committee are professional people.

Could I use the binomial distribution on this question?

x = number of professionals in a committe of 10 people. X ~(10, 14/22)

a) p(x=6)

Originally Posted by Tweety

A committee of size 10 is selected at random from 14 professional people and 8 are non-professional people. what is the probability that;
a) Exactly 6 members of the committee are professional people?
b) No more than 3 members of the committee are professional people.
Could I use the binomial distribution on this question?
x = number of professionals in a committe of 10 people. X ~(10, 14/22)
a) p(x=6)

NO

This is sampling without replacement, so that does not apply..

There are $\displaystyle \binom{22}{10}$ total ways to select the committee.

There are $\displaystyle \binom{14}{6}\binom{8}{4}$ ways for $\displaystyle x=6~.$