Question

If a couple plans to have 5 children, what is the probability that there will be at least one boy? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one boy in 5 children? The probability is (Type an integer or a simplified fraction.)
Please answer both questions

Answer 1

From the given information,

Here,

Sample size (n)=5

Probability of success (p)=0.5

Hence,

Using binomial probability calculater,

Binomial Distribution X ~ Bin(n,p) p= 0.5 P(X 2 x) = 0.96875 P(X=x) 0 1 2 3 4 u= E(X) = 2.5 0 = SD(X) = 1.118 m2 = Var(X) = 1.25

Hence,

Required probability is,

P(X≥1)=0.9688

As this probability very close to 1,

Hence, probability is high enough for the couple to be very confident that they will get at least one boy in 5 children.

Thank you.