To find the probability that a boy will win the quiz competition, follow these steps:
1. Determine the total number of participants:
- There are 12 boys.
- There are 12 girls.
- Therefore, the total number of participants is [tex]\( 12 + 12 = 24 \)[/tex].
2. Determine the number of favorable outcomes:
- The favorable outcomes are the scenarios where a boy wins.
- There are 12 boys, so there are 12 favorable outcomes.
3. Calculate the probability:
- The probability [tex]\( P \)[/tex] of an event occurring is given by the formula:
[tex]\[
P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}
\][/tex]
- Here, the number of favorable outcomes (a boy winning) is 12, and the total number of outcomes (all participants) is 24.
4. Plug in the values:
- Using the formula:
[tex]\[
P = \frac{12}{24}
\][/tex]
5. Simplify the fraction:
- Simplifying [tex]\( \frac{12}{24} \)[/tex]:
[tex]\[
\frac{12}{24} = \frac{1}{2}
\][/tex]
Therefore, the probability that a boy will win the quiz competition is [tex]\(\frac{1}{2}\)[/tex].
