What is the theoretical probability of the event that a family with two children has two boys?
$\frac{1}{2}$
$\frac{1}{4}$
$\frac{1}{6}$
$\frac{1}{8}$
Please select the best answer from the choices provided.
Answer (1)
List all possible outcomes: (Boy, Boy), (Boy, Girl), (Girl, Boy), (Girl, Girl).
Identify the favorable outcome: (Boy, Boy).
Calculate the probability: 4 1 .
The theoretical probability of having two boys is 4 1 .
Explanation
Understand the problem Let's break down the problem. We want to find the probability that a family with two children has two boys. To do this, we need to consider all the possible combinations of genders for the two children.
List all possible outcomes The possible outcomes for the genders of two children are:
Boy, Boy (BB)
Boy, Girl (BG)
Girl, Boy (GB)
Girl, Girl (GG)
There are a total of 4 possible outcomes.
Determine the number of favorable outcomes We are interested in the event where both children are boys (BB). There is only 1 outcome where this occurs.
Calculate the probability The probability of having two boys is the number of favorable outcomes divided by the total number of possible outcomes. In this case, it is 4 1 .
State the final answer Therefore, the theoretical probability of a family with two children having two boys is 4 1 .
Examples
Imagine you're flipping two coins. What's the chance of getting heads on both? This is similar to figuring out the probability of a family having two boys. Each coin flip has two possibilities (heads or tails), just like each child has two possibilities (boy or girl). Calculating these probabilities helps in understanding genetics, predicting simple events, and even making informed decisions in games of chance.
