If there is an equal probability of a child being born a boy or a girl, what is the probability that...
If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 8 children have two children of the same sex and one of the opposite sex?
Answer/Solution
1/16
Steps/Work
No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 8 = 8C2
Total possible outcomes - 2^8 (each child can be either a girl or a boy)
Probability=2C1*8C2/2^8= 2*8/2*2*2*2*2*2*2*2=16/256=1/16
Ans=D
No of ways of selecting any 2 children out of 8 = 8C2
Total possible outcomes - 2^8 (each child can be either a girl or a boy)
Probability=2C1*8C2/2^8= 2*8/2*2*2*2*2*2*2*2=16/256=1/16
Ans=D