Use the hypergeometric PDF formula to find the probability r

Use the hypergeometric PDF formula to find the probability requested. Check your answer by using Excel. (Round your answers to 4 decimal places.) i. N = 14, n = 2, s = 6, P(X = 1) ii. N = 25, n = 8, s = 6, P(X = 5) iii. N = 41, n = 3, s = 8, P(X = 2) iv. N = 57, n = 5, s = 10, P(X = 4) i. P(X = 1) ii. P(X = 5) iii. P(X = 2) iv. P(X = 4)

Solution

I.

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 =    14      
K = number of successes in the population =    6      
n = sample size =    2      
x = number of successes in the sample =    1      
          
Thus,          
          
P(   1   ) =    0.527472527 [ANSWER]

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ii.

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 =    25      
K = number of successes in the population =    6      
n = sample size =    8      
x = number of successes in the sample =    5      
          
Thus,          
          
P(   5   ) =    0.005375494 [ANSWER]

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iii.

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 =    41      
K = number of successes in the population =    8      
n = sample size =    3      
x = number of successes in the sample =    2      
          
Thus,          
          
P(   2   ) =    0.086679174 [ANSWER]

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iv.

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 =    57      
K = number of successes in the population =    10      
n = sample size =    5      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.002357237 [ANSWER]

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