Question

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men is ______.

विकल्प

• `21/220`

• `3/11`

• `1/11`

• `2/23`

Answer 1

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men is `underlinebb(1/11)`.

Explanation:

Probability of 4 member committee which contain atleast one woman.

⇒ P(3M, 1W) + P(2M, 2W) + P(1M, 3W) + P(0M, 4W)

`(""^10"C"_3  ""^5"C"_1)/(""^15"C"_4) + (""^10"C"_2  ""^5"C"_2)/(""^15"C"_4) + (""^10"C"_1  ""^5"C"_3)/(""^15"C"_4) + (""^10"C"_0  ""^5"C"_4)/(""^15"C"_4)`

`600/1365 + 450/1365 + 100/1365 + 5/1365` = `1155/1365`

∴ Probability of committees to have more women than men.

= `("P"(1"M", 3"W") + "P"(0"M", 4"W"))/("P"(3"M", 1"W") + "P"(2"M", 2"W") + "P"(1"M", 3"W") + "P"(0"M", 4"W"))`

= `(105/1365)/(1155/1365)`

= `1/11`