SOLUTION: In a random selected family of three biologically theirs, normally conceived children, find the probability that this family has: A.) all children of the same gender B.) Only tw

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Question 1144390: In a random selected family of three biologically theirs, normally conceived children, find the probability that this family has:
A.) all children of the same gender
B.) Only two children of the same gender
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

            Assuming that the probability to have in a family a boy  (B)  or a girl  (G)  is   1%2F2 


(A)  The probability that all 3 children are of the same gender =     


         = The probability of  %281%2F2%29%2A%281%2F2%29%2A%281%2F2%29 = 1%2F8  to have 3 girls 

     PLUS

           the probability of  %281%2F2%29%2A%281%2F2%29%2A%281%2F2%29 = 1%2F8  to have 3 boys =


     = 1%2F8 + 1%2F8 = 2%2F8 = 1%2F4.    ANSWER




(B)  P = P(BBG) + P(BGB) + P(GBB) + P(GGB) + P(GBG) + P(GGB) = 6%2F8 = 3%2F4.     ANSWER



Notice that the probability of the n.B  is the complement to the probability of the n.A, as it should be.


It is an additional argument/check that the solution is correct.

Solved.