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The problem asks for the probability of Kathy having **at most one son** if she were to have four children, assuming that the probability of having a boy or a girl is equal (i.e., 50% for each gender).

### Step-by-step solution:

1. **Determine the total number of outcomes**: 
   Since each child can either be a boy or a girl, and there are 4 children, the total number of possible outcomes is:
   \[
   2^4 = 16
   \]
   Each outcome corresponds to a unique sequence of boys (B) and girls (G) in the family.

2. **At most one son**:
   This includes the cases where Kathy has:
   - 0 sons (all girls),
   - 1 son (exactly one boy).

3. **List the possible outcomes**:
   - **0 sons**: The only possibility is all girls: GGGG.
   - **1 son**: There are 4 possible outcomes where exactly one child is a boy:
     - BGGG
     - GBGG
     - GGBG
     - GGGB

4. **Count the favorable outcomes**:
   The favorable outcomes are the ones listed above:
   - 1 outcome for 0 sons,
   - 4 outcomes for 1 son.
   In total, there are \( 1 + 4 = 5 \) favorable outcomes.

5. **Probability calculation**:
   The probability of having at most one son is the ratio of favorable outcomes to the total number of outcomes:
   \[
   \frac{5}{16}
   \]

Therefore, **the probability is \( \frac{5}{16} \)**.

Would you like more details or have any other questions?

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Here are 5 related questions for further practice:
1. What is the probability of having exactly two sons out of four children?
2. What is the probability of having at least one son out of four children?
3. What is the probability of having three sons and one daughter?
4. If Kathy had five children, what would be the probability of having at most one son?
5. How does the probability change if the probability of having a son were different from 50%?

**Tip**: For probability questions involving multiple independent events (like this one), using binomial distribution formulas can also be very efficient.

Assuming that boy and girl babies are equally likely, what would be Kathy's probability of having at most one son if she were to have four children altogether?

Understand how to calculate the probability of having at most one son in a family of four children. This problem involves concepts such as probability, binomial distribution, and combinatorics. Suitable for students in Grades 9-12.

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