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A committee of 5 people is selected at random from a group of 16 men and 12 women. Find the probability that the committee contains at least 2 women. 

 Feb 19, 2020
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At least  2 women means that the committee  contains 2, 3, 4  or 5 women

 

P(2 women)  = C(16,3) * C(12, 2)  / C(28,5)

 

P(3 women)  = C(16,2) * C(12,3) / C(28,5)

 

P(4 women) =  C(16,1) * C(12,4) / C(28,5)

 

P(5 women ) =  C(12,5) / C ( 28,5)

 

So....the total probability  is

 

 [ C(16,3)* C(12,2)  + C(16,2)*C(12,3)  + C(16,1) * C(12,4)  + C(12,5) ] / C(28,5)    = 

 

 11  / 15  

 

 

cool cool cool

 Feb 19, 2020

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