You select a family with three 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 shown below. Find the probability of selecting a family with at least three male children.
The probability of having at least three male children is (Type an integer or a simplified fraction.)

Step 1 ：The problem is asking for the probability of a family with three children having at least three male children. This means we are looking for the probability of having exactly three male children, as it's not possible to have more than three male children in a family with only three children.

Step 2 ：The set of equally likely outcomes for the children's genders includes all possible combinations of male and female children in a family with three children. This would be: MMM, MMF, MFM, FMM, MFF, FMF, FFM, FFF.

Step 3 ：There are \(8\) possible outcomes in total, and only one of these outcomes (MMM) represents a family with at least three male children.

Step 4 ：So, the probability of selecting a family with at least three male children is \(1\) out of \(8\), or \(\frac{1}{8}\).

Step 5 ：Final Answer: The probability of selecting a family with at least three male children is \(\boxed{\frac{1}{8}}\).