As men and women age, their risk of death increases. There are also health issue

Question

As men and women age, their risk of death increases. There are also health issues that can greatly impair older citizens' abilities to participate in activities and travel. Assume you are planning a 60th high school reunion and are wondering how many of the older adults would be able to attend. If you know that 27 women and 23 men are still alive, and are told that exactly 12 of them will attend, what is the probability that you would have exactly six men and exactly six women attend? (round to four decimal places.)

Explanation / Answer

Let a success be getting a man.

There are 50 alive, 23 are men.

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 =    50      
K = number of successes in the population =    23      
n = sample size =    12      
x = number of successes in the sample =    6      
          
Thus,          
          
P(   6   ) =    0.246140093 [ANSWER]

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