SOLUTION: A household with three children is selected randomly. The children are reported according to their gender and serial number of their birth. What is the probability that the househo

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Question 854698: A household with three children is selected randomly. The children are reported according to their gender and serial number of their birth. What is the probability that the household has 2 boys. Show the calculation.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

three children: p(boy) = 1/2, p(girl) = 1/2

May use Binomial Distribution Formula:P+%28x%29=+highlight_green%28nCx%29%28p%5Ex%29%28q%29%5E%28n-x%29+ 

P(x = 2 boys) = 3%281%2F2%29%5E2%281%2F2%29%5E1+=+3%2F8      |Note 3C2 = 3

Or counting

Note: 3 possible outcomes for the order 2 boys were born, P = 1/8 for each of them

GBB

BGB

BBG

P(x = 2 boys) = 3%281%2F8%29+=+3%2F8