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probability

by pappueshwar » Sun Mar 11, 2012 9:59 am
The probability of a new born baby is a boy is 50% and that of a new born baby is a girl is 50%. Ten mothers are going to give birth to ten babies this morning. What is the probability that at least two babies are boys?

i dont have options.... can any one assist with solution
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by pemdas » Sun Mar 11, 2012 1:48 pm
pappueshwar wrote:The probability of a new born baby is a boy is 50% and that of a new born baby is a girl is 50%. Ten mothers are going to give birth to ten babies this morning. What is the probability that at least two babies are boys?

i dont have options.... can any one assist with solution
even if one hundred moms will give birth to one hundred babies the probability won't change and will stay the same 50% boy vs. girl for 100 replications. Hence P(at least 2 boys)=P(2 boys)+P(3 boys)+...P(10 boys) or find the complement P(at least 2 boys)=1-P(No boys)-P(1 boy)

P(No boys)=(0.5)^10 and here only one way. Now to find P(1 boy) we will use combination of 10C1 ways for each of one boy success birth rate -> (10C1)*(0.5)^10=10*(1/32)^2=
= 10/1024=5/512

Thus, P(at least 2 boys)=1 -1/1024 -5/512= (1024-1-10)= 1013/1024
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