SOLUTION: In a family with 4 children, the number of children with blue eyes is a binomial random variable X with n=4 and p=.20. What is the probability that all 4 children with have blue

Question 324558: In a family with 4 children, the number of children with blue eyes is a binomial random variable X with n=4 and p=.20.
What is the probability that all 4 children with have blue eyes?
What is the probability that exactly 3 children will have blue eyes?
What is the probability that none of the children with have blue eyes?
What is the expected number of children with blue eyes, E(X)?
What is the variance for teh number of children with blue eyes, V(X)?
Any help would be greatly appreciated.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a family with 4 children, the number of children with blue eyes is a binomial random variable X with n=4 and p=.20.
What is the probability that all 4 children with have blue eyes?;;;(0.2)^4
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What is the probability that exactly 3 children will have blue eyes?
4C3(0.2)^3(0.8) = 0.0256
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What is the probability that none of the children with have blue eyes?;;;0.8^4
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What is the expected number of children with blue eyes, E(X)= np = 0.2*4 = 0.8
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What is the variance for the number of children with blue eyes, V(X) = npq=0.64
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Cheers,
Stan H.
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