A pool of 10 semifinalists for a job consist of 7 women and

A pool of 10 semifinalists for a job consist of 7 women and 3 men. To find 2 finalists, the names of two of the semifinalists are drawn, one after the other, at random.

a) What is the probability that both finalists are men?

b) What is the probability that one finalist is a woman and the other a man?

Solution

Let the \"success\" here is getting a male.

a)

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 =    10      
K = number of successes in the population =    3      
n = sample size =    2      
x = number of successes in the sample =    2      
          
Thus,          
          
P(   2   ) =    0.066666667 [ANSWER]

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b)

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 =    10      
K = number of successes in the population =    3      
n = sample size =    2      
x = number of successes in the sample =    1      
          
Thus,          
          
P(   1   ) =    0.466666667 [ANSWER]