Thread: A club has members; Find probability

1. A club has members; Find probability

A club has 6 women and 6 men members. A committee of 6 is chosen randomly. What is the probability that the committee contains more women than men. Simplify into a fraction into a fraction in lowest terms (show off cancellations).

Thank you so much!!

2. Originally Posted by bjanela

A club has 6 women and 6 men members. A committee of 6 is chosen randomly. What is the probability that the committee contains more women than men. Simplify into a fraction into a fraction in lowest terms (show off cancellations).

Thank you so much!!
I would start by determining what the probability is that the committee contains equal amounts of men and women. Since the committee draws from an equal amount of men and women, then the chances the remaining fraction contains more women than men must be half of that.

I suppose your other option would be to find the probability of there being 4 women, 5 women, and 6 women, and adding them together, but this seems like more work to me.

3. Originally Posted by TravisH82
I would start by determining what the probability is that the committee contains equal amounts of men and women. Since the committee draws from an equal amount of men and women, then the chances the remaining fraction contains more women than men must be half of that.

[snip]
Clarification: If the probability "that the committee contains equal amounts of men and women" is p, then the probability that the committe contains more women than men will be (1 - p)/2.

Note that $p = \frac{{6 \choose 3} {6 \choose 3}}{{12 \choose 6}}$.