Hyper geometric N NR Ex N 30 NR Females 10 R Females r 5

Hyper geometric: N N-R Ex: N = 30 N-R = Females 10 = R Females r = 5 X = # f females or the committee.

Solution

For x = 0:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    30      
K = number of successes in the population =    10      
n = sample size =    5      
x = number of successes in the sample =    0      
          
Thus,          
          
P(   0   ) =    0.108795419 [ANSWER]

************

For x = 1:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    30      
K = number of successes in the population =    10      
n = sample size =    5      
x = number of successes in the sample =    1      
          
Thus,          
          
P(   1   ) =    0.339985685 [ANSWER]

************

For x = 2:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    30      
K = number of successes in the population =    10      
n = sample size =    5      
x = number of successes in the sample =    2      
          
Thus,          
          
P(   2   ) =    0.359984843 [ANSWER]

**********

For x = 3:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    30      
K = number of successes in the population =    10      
n = sample size =    5      
x = number of successes in the sample =    3      
          
Thus,          
          
P(   3   ) =    0.159993263 [ANSWER]

*********

For x = 4:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    30      
K = number of successes in the population =    10      
n = sample size =    5      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.029472443 [ANSWER]

*******

For x = 5:

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    30      
K = number of successes in the population =    10      
n = sample size =    5      
x = number of successes in the sample =    5      
          
Thus,          
          
P(   5   ) =    0.001768347 [ANSWER]

Hence, we have the table:

x	P(x)
0	0.108795
1	0.339986
2	0.359985
3	0.159993
4	0.029472
5	0.001768