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, ffmm, fmfm, fmmf, fmmm, mfmm, mmfm, mmmf, mmmm}. find the probability of selecting a family with exactly three female children.

the probability of having exactly three female children is \boxed{}.
(type an integer or a simplified fraction.)

Explanation:

Step1: Count total outcomes

Total outcomes = 16 (given set size)

Step2: Count favorable outcomes

Favorable outcomes (3F,1M): FFFM, FFMF, FMFF, MFFF → 4 outcomes

Step3: Calculate probability

Probability = $\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{4}{16} = \frac{1}{4}$

Answer:

$\frac{1}{4}$