If a couple plans to have 9 children, what is the probability that there will be

Question

If a couple plans to have 9 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 9 children The probability is. (Type an integer or a simplified fraction.)Can the couple be very confident that they will have at least one boy No because the probability is close to 1.No because the probability is close to 0. Yes because the probability is close to 0.Yes because the probability is close to 1.

Explanation / Answer

Binomial Distribution

Solution:

Here, we are given, n = 9 and p = 0.5 since boys and girls have equally chance

Here, we have to find P(X1)

P(X1) = 1 – P(X<1) = 1 – P(X=0)

P(X=0) = 9C0 * 0.5^0 * (1 – 0.5)^(9 – 0) = 1*0.5^0 * 0.5^9

P(X=0) = 1*1*0.001953

P(X=0) = 0.001953

P(X1) = 1 – P(X<1) = 1 – P(X=0) = 1 – 0.001953 = 0.998047

Required probability = 0.998047

The couple would be very confident that they will have at least one boy because

D) Yes, because the probability is close to 1.

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