Question
Assuming boys and girls are equally likely, find the probability of a couple having a baby boy when their fifth child is born, given that the first four children were all boys. The probability is \( \square \). (Type an integer or a simplified fraction.)
Ask by Adkins Hall. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability is \(\frac{1}{2}\).
Solution
The probability of having a boy or a girl for each child is independent of previous births. Since boys and girls are equally likely, the probability remains the same for each birth regardless of the outcomes of the previous children.
Therefore, the probability that the fifth child is a boy is:
\[
\frac{1}{2}
\]
**Answer:** \(\frac{1}{2}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The probability of having a boy or a girl for each individual child is always \( \frac{1}{2} \), regardless of previous siblings. Therefore, the probability of the couple having a baby boy when their fifth child is born remains \( \frac{1}{2} \). Thus, the probability is \( \frac{1}{2} \).
