Question
In a class, there are 30 girls and 15 boys. 20 of the 30 girls like football and the rest of them like badminton. 10 of the 15 boys like football and the rest of them like badminton. Find the probability that the student selected randomly will be a boy who likes football? Reduce the fraction. (1 point) Responses 110 1 tenth 1 1 29 2 ninths 13
Answers
GPT-4o mini
To find the probability that a randomly selected student is a boy who likes football, we need to follow these steps:
1. **Calculate the total number of students:**
\[
\text{Total students} = \text{girls} + \text{boys} = 30 + 15 = 45
\]
2. **Identify the number of boys who like football:**
According to the problem, there are 10 boys who like football.
3. **Calculate the probability:**
The probability \( P \) of selecting a boy who likes football is given by the ratio of the number of boys who like football to the total number of students:
\[
P(\text{boy who likes football}) = \frac{\text{Number of boys who like football}}{\text{Total number of students}} = \frac{10}{45}
\]
4. **Reduce the fraction:**
We can simplify \( \frac{10}{45} \) by dividing the numerator and the denominator by their greatest common divisor, which is 5:
\[
\frac{10 \div 5}{45 \div 5} = \frac{2}{9}
\]
Therefore, the probability that a randomly selected student will be a boy who likes football is \( \frac{2}{9} \).
1. **Calculate the total number of students:**
\[
\text{Total students} = \text{girls} + \text{boys} = 30 + 15 = 45
\]
2. **Identify the number of boys who like football:**
According to the problem, there are 10 boys who like football.
3. **Calculate the probability:**
The probability \( P \) of selecting a boy who likes football is given by the ratio of the number of boys who like football to the total number of students:
\[
P(\text{boy who likes football}) = \frac{\text{Number of boys who like football}}{\text{Total number of students}} = \frac{10}{45}
\]
4. **Reduce the fraction:**
We can simplify \( \frac{10}{45} \) by dividing the numerator and the denominator by their greatest common divisor, which is 5:
\[
\frac{10 \div 5}{45 \div 5} = \frac{2}{9}
\]
Therefore, the probability that a randomly selected student will be a boy who likes football is \( \frac{2}{9} \).