Answer with explanation:
Number of children in the family = 4
It is also given that, f represents female child and m represents male child.
Total Possible outcome ={ffff, fffm, ffmf, fmff, mfff, mffm, mfmf, mmff, ffmm, fmfm, fmmf, fmmm, mfmm, mmfm, mmmf, m m mm}=16
Total favorable outcome = Selecting a family with exactly three male children
= { fmmm, mfmm, mmfm, mmmf}=4
Probability of an event
[tex]=\frac{\text{Total favorable outcome}}{\text{Total Possible outcome}}\\\\=\frac{4}{16}\\\\=\frac{1}{4}[/tex]
or there is other way of looking at this question.
If a family has only three children, then
Total possible Outcome =1 +1+3+3=8 possible outcome={f ff,f m f,f f m,m ff,m m f,m f m,f mm,m mm}
Total favorable outcome ={m mm}=1
Probability of an event
[tex]=\frac{\text{Total favorable outcome}}{\text{Total Possible outcome}}\\\\\frac{1}{8}[/tex]
