Question

you select a family with four children. if m represents a male child and f a female child, the set of equally likely outcomes for the childrens genders is {ffff, fffm, ffmf, fmff, mfff, mffm, mfmf, mmff, f fmm, fmfm, fmmf, fmmm, mfmm, mmfm, mmmf, mmmm}. find the probability of selecting a family with exactly zero male children. the probability of having exactly zero male children is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of favorable outcomes

The favorable outcome (exactly zero male children) is \(\{FFFF\}\), so the number of favorable outcomes \(n = 1\).

Step2: Determine the total number of outcomes

The set of all outcomes has \(N=16\) elements.

Step3: Calculate the probability

The probability formula is \(P=\frac{n}{N}\). Substituting \(n = 1\) and \(N = 16\), we get \(P=\frac{1}{16}\).

Answer:

\(\frac{1}{16}\)