SOLUTION: The Mississauga Valley Bridge Club has 15 members: 10 women and 5 men. A committee of 6 people is selected from the club. a) What is the probability that the committee contains

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Question 1200601: The Mississauga Valley Bridge Club has 15 members: 10 women and 5 men. A committee of 6 people is selected from the club.
a) What is the probability that the committee contains no women?
b) What is the probability that the committee contains exactly 2 women?
c) What is the probability that the committee contains at least 3 women?
Answer by GingerAle(43) About Me  (Show Source):
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**a) Probability of no women in the committee**
* **Total possible committees:** 15C6 = 5005 (combinations of 15 people taken 6 at a time)
* **Committees with only men:** 5C6 = 1 (there are only 5 men, so only one combination of 6 men exists)
* **Probability:** 1 / 5005 = 0.0002
**b) Probability of exactly 2 women in the committee**
* **Ways to choose 2 women:** 10C2 = 45
* **Ways to choose 4 men:** 5C4 = 5
* **Total combinations with 2 women:** 45 * 5 = 225
* **Probability:** 225 / 5005 = 0.045
**c) Probability of at least 3 women in the committee**
* **Find the probability of 0, 1, or 2 women:**
* Probability of 0 women: 0.0002 (calculated in part a)
* Probability of 1 woman: (10C1 * 5C5) / 5005 = 10 / 5005 = 0.002
* Probability of 2 women: 0.045 (calculated in part b)
* **Probability of at least 3 women:** 1 - (0.0002 + 0.002 + 0.045) = 1 - 0.0472 = 0.9528
**Therefore:**
* **a) Probability of no women:** 0.0002
* **b) Probability of exactly 2 women:** 0.045
* **c) Probability of at least 3 women:** 0.9528