Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is [tex]$\frac{1}{2}$[/tex]. What is the probability that the next child born to the same family will also be a girl?
A. [tex]$\frac{1}{2}$[/tex]
B. [tex]$\frac{1}{4}$[/tex]
C. [tex]$\frac{1}{8}$[/tex]
D. [tex]$\frac{1}{12}$[/tex]
Please select the best answer from the choices provided.
Answer (2)
Each birth is an independent event.
The probability of a girl being born is 2 1 .
The probability of the next child being a girl is independent of previous births.
Therefore, the probability that the next child will be a girl is 2 1 .
Explanation
Understand the problem and provided data The problem states that the birth of a boy or a girl is equally likely, and the probability of a single child being born a girl is 2 1 . We are asked to find the probability that the next child born to the same family will also be a girl.
Independent events Since each birth is an independent event, the probability of the next child being a girl is independent of any previous births. This means that the outcome of previous births does not affect the probability of the next birth being a girl.
Determine the probability Therefore, the probability that the next child will be a girl is 2 1 .
Final Answer The probability that the next child born to the same family will also be a girl is 2 1 .
Examples
Imagine you're flipping a coin. Each flip is independent of the previous ones. Even if you've flipped heads five times in a row, the probability of getting heads on the next flip is still 2 1 . Similarly, the gender of a child is independent of the gender of previous children. So, even if a family has several boys, the probability of their next child being a girl remains 2 1 .
The probability that the next child born to the same family will be a girl is 2 1 because each birth is an independent event. The gender of previous children does not affect the probability of the next child. Therefore, the correct answer is 2 1 .
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