Probability of Selecting All Women in a Group of 5 from a Room of 100 People

[zzinfinity]

Suppose I have a room of 100 people, 10 of which are women. What is the probability that a group of 5, selected at random, are all women.

Is it (.1)^5 or is it (10/100)*(9/99)*(8/98)*(7/97)*(6/96). Or is it something else? Also any references to help me understand this question better would be greatly appreciated!

 

[phinds]

Second one looks right to me

 

[Bacle2]

The probability, assumming each woman is equally-likely to be selected is:

# of ways of choosing 5 women / # of ways of choosing any 5 people, which

agrees with your second answer. The first answer is true if you had "replacement",

i.e., if every time a woman was selected, she would go back into the pool. But

once you select a woman I imagine you select the second, etc., from the remaining

ones, so that the probability of selecting is not always 0.1; it changes every time

one is selected, which is reflected in your second answer.

BTW, the more formal way is doing the ratio: 10C5 / 100C5

where nCm := n!/(m!(n-m)!).