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, ffme, fmff, mffe, mffm, mfme, mmff, ffmm, fmfm, fmmf, fmmm, mfmm, mmfm, mmmf, mmmm}. find the probability of selecting a family with exactly four female children. the probability of having exactly four female children is (type an integer or a simplified fraction.)

Explanation:

Step1: Count the total number of outcomes

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

Step2: Count the number of favorable outcomes

The outcome with exactly four female children is \(FFFF\), so \(m=1\).

Step3: Calculate the probability

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

Answer:

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