homework help! committee question

D

davidh

New member
Joined
Dec 8, 2020
Messages
12
The Valley Bridge Club has 15 members: 10 women and 5 men. A committee of 6 people is selected from the club.

What is the probability that the committee contains exactly 2 women?
15c6= 5005 is the total
10x2x5c3/5005 = 8.99% but thats not an option where did i go wrong?

What is the probability that the committee contains at least 3 women?
10c3x5c2+10c4X5c1 + 10C5X5C0 /5005 wrong answer again 49.99% but closest option is 50.3%

What is the probability that the committee contains no women?
this would be 0% as there are only 5 men in a committee of 6
 
Hypergeometric Multinomial distribution
2 groups: 5 men, 10 women

exactly 2 women means 4 men, 2 women

[MATH]P[\text{exactly 2 women}] = \dfrac{\dbinom{5}{4}\dbinom{10}{2}}{\dbinom{15}{6}} =\dfrac{45}{1001}\approx 4.5\%[/MATH]
For at least 3 women you need to sum up the probabilities of the 3/3, 2/4, 1/5, and 0/6 cases, or
perhaps easier sum up the probabilities of the 5/1, 4/2 cases and subtract that from 1

Yes. It's impossible to select 6 men from 5 total.
 
Romsek said:
Hypergeometric Multinomial distribution
2 groups: 5 men, 10 women

exactly 2 women means 4 men, 2 women

[MATH]P[\text{exactly 2 women}] = \dfrac{\dbinom{5}{4}\dbinom{10}{2}}{\dbinom{15}{6}} =\dfrac{45}{1001}\approx 4.5\%[/MATH]
For at least 3 women you need to sum up the probabilities of the 3/3, 2/4, 1/5, and 0/6 cases, or
perhaps easier sum up the probabilities of the 5/1, 4/2 cases and subtract that from 1

Yes. It's impossible to select 6 men from 5 total.
Click to expand...
what do you mean by 5/1 and 4/2 cases?

do you mean 5C1 X4C2 =1- 30/5005 =99.4%?
 
davidh said:
i keep getting 99% even after -1
Click to expand...

yer killin me Smalls

[MATH] P[\text{at least 3 women}] = 1 - P[\text{4 men, 2 women}]- P[\text{5 men, 1 woman}] = \\ 1 - \dfrac{\dbinom{5}{4}\dbinom{10}{2}}{\dbinom{15}{6}} - \dfrac{\dbinom{5}{5}\dbinom{10}{1}}{\dbinom{15}{6}} = \dfrac{911}{1001} \approx 91\%\\ [/MATH]
 
You must log in or register to reply here.
Top