Is this Binomial Distribution? How do i even identify if it is?

pbrain26

New member
A board of directors consists of eight men and four women.
A four-member search committee is randomly chosen to recommend a new company president.
What is the probability that all four members of the search committee will be women?

MarkFL

Super Moderator
Staff member
I would just compute the number of ways all 4 women can be chosen and divide by the number of ways to choose 4 from 12.

pbrain26

New member
I would just compute the number of ways all 4 women can be chosen and divide by the number of ways to choose 4 from 12.
Sooo are the number of ways all 4 women can be chosen, is it 4/12 ^4 ?

MarkFL

Super Moderator
Staff member
Sooo are the number of ways all 4 women can be chosen, is it 4/12 ^4 ?
Since there are only 4 women in the board of directors, there is only one way to choose 4 women, namely to choose all of them, since order doesn't matter here. Now, for computing the number of ways to choose 4 from 12, we may use:

$$\displaystyle {12 \choose 4}=\frac{12!}{4!(12-4)!}$$

Can you proceed?

JeffM

Elite Member
The binomial distribution applies to the probability of events that are independent.

Is the probability that the second person selected is a woman independent of the probability that the first person selected is a woman?