You select a family with four children. If $\mathrm{M}$ represents a male child and $\mathrm{F}$ a female child, the set of equally likely outcomes for the children's 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 one female child
The probability of having exactly one female child is (Type an integer or a simplified fraction.)
Answer
\(\boxed{\frac{1}{4}}\) is the final answer.
Step 1 ：Define the set of equally likely outcomes for the children's genders as [FFFF, FFFM, FFMF, FMFF, MFFF, MFFM, MFMF, MMFF, FFMM, FMFM, FMMF, FMMM, MFMM, MMFM, MMMF, MMMM].
Step 2 ：Count the total number of outcomes, which is 16.
Step 3 ：Identify the outcomes where there is exactly one female child: MFFF, FMFF, FFMF, FFFM.
Step 4 ：Count the number of these outcomes, which is 4.
Step 5 ：Calculate the probability of selecting a family with exactly one female child by dividing the number of desired outcomes by the total number of outcomes, which is \(\frac{4}{16} = \frac{1}{4}\).
Step 6 ：\(\boxed{\frac{1}{4}}\) is the final answer.
