Question

you select a family with three children. if m represents a male child, and f represents a female child, the set of equally likely outcomes for the childrens genders is {mmm, mmf, mfm, mff, fmm, fmf, ffm, fff}. find the probability of selecting a family with 4 male children. p(4 male children) = (type an integer or a simplified fraction)

Explanation:

Step1: Determine the number of favorable outcomes

The set of outcomes is \(\{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF\}\). There are no outcomes with 4 male children. So the number of favorable outcomes \(n = 0\).

Step2: Determine the total number of outcomes

Count the elements in the set \(\{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF\}\). The total number of outcomes \(N=8\).

Step3: Use the probability formula

The probability formula is \(P=\frac{n}{N}\). Substitute \(n = 0\) and \(N = 8\) into the formula: \(P=\frac{0}{8}\).

Answer:

\(0\)