Assume that that it is equally likely for a child to be born

Assume that that it is equally likely for a child to be born a boy or a girl, and that the Obama family is planning on having three children. Compute the probability that the Obamas will have two boys and one girl

Solution

Let a success be having a boy.

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    3      
p = the probability of a success =    0.5      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.375 [ANSWER]