The theoretical probability of a couple having a baby girl is [tex]$\frac{1}{2}$[/tex]. What is [tex]$P$[/tex](girl, girl, girl)?
A. [tex]$\frac{1}{8}$[/tex]
B. [tex]$\frac{1}{6}$[/tex]
C. [tex]$\frac{1}{3}$[/tex]
D. [tex]$\frac{3}{8}$[/tex]
Answer (1)
The probability of having a baby girl is 2 1 .
Each birth is an independent event.
The probability of having three girls in a row is ( 2 1 ) 3 .
The probability of having three girls in a row is 8 1 .
Explanation
Understand the problem The problem states that the theoretical probability of a couple having a baby girl is 2 1 . We are asked to find the probability of the couple having three girls in a row.
Independent events Since each birth is an independent event, the probability of having three girls in a row is the product of the probabilities of having a girl in each birth.
Calculate the probability The probability of having a girl is 2 1 for each birth. Therefore, the probability of having three girls in a row is:
Final Calculation 2 1 × 2 1 × 2 1 = ( 2 1 ) 3 = 8 1 Thus, the probability of having three girls in a row is 8 1 .
State the final answer The probability of a couple having three girls in a row is 8 1 .
Examples
This type of probability calculation is useful in genetics to predict the likelihood of inheriting certain traits. For example, if a certain gene has a 50% chance of being passed down, you can calculate the probability of a child inheriting that gene from both parents or multiple children inheriting the gene. This helps in understanding the distribution of traits within families and populations. The same logic applies in other scenarios where independent events occur sequentially, such as predicting the outcomes of coin flips or other random processes.
