You select a family with three children. If M represents a male child, and F represents a
female child, the set of equally likely outcomes for the children’s genders is (MMMM,
MMF, MFM, MFF, FMM, FMF, FFM, FFF). Find the probability of selecting a family with 6
male children.
male children
(Type an integer or a simplified fraction.)

Question

You select a family with three children. If M represents a male child, and F represents a
female child, the set of equally likely outcomes for the children’s genders is (MMMM,
MMF, MFM, MFF, FMM, FMF, FFM, FFF). Find the probability of selecting a family with 6
male children.

male children

(Type an integer or a simplified fraction.)

UpStudy AI · Accepted Answer

**Step 1: Understand the Problem**

The problem states that a family is selected with three children, and the set of equally likely outcomes is given (although there is a typographical error in the provided list, the correct outcomes should be those for three children, such as $$ \{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF\} $$).

**Step 2: Analyze the Event of Interest**

We are asked to find the probability of selecting a family with 6 male children. Since the family only has three children, it is impossible for a family with three children to have 6 male children.

**Step 3: Conclusion**

Since the event (having 6 male children) cannot occur with a family of three children, its probability is $$ 0 $$.

$$
P(6 \text{ male children}) = 0
$$
The probability of selecting a family with 6 male children is 0.

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