Question

A commitee is consist of 6 men and 4 woman ,a sub commitee is made by randomly choosen three commitee members .what is the probability that(a)they are all woman (b) two of them are men

Answer 1

a) 1/30

b) 1/6

Explanation:

a) There are 10 people total and a group of 3 is being chosen. However, they all need to be women:

For the first person, the probability of it being a woman is 4/10

For the second person, the probability of it being a woman (with the prerequisite that the first was a woman) is 3/9

For the third (with the same requirements) is 2/8

If we multiply all of the fractions together, we get:
`(1)/(30)`

b) There are 10 people total and a group of 3 is being chosen. However, two of them need to be men, and 1 needs to be a woman:

For the first person, the probability of it being a man is 6/10

For the second person, the probability of it being a man (with the prerequisite that the first was a man as well) is 5/9

For the third person, the probability of it being a woman (because it can only be two men) is 4/8

If we multiply all the fractions together, we get:
`(1)/(6)`