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?

Question

Reduce the fraction.

(1 point)
Responses

292 ninths

131 third

1101 tenth

1
1

Answer 1

To find the probability that a randomly selected student is a boy who likes football, we can follow these steps:

1. Determine the total number of students.

   • Total number of girls = 30
   • Total number of boys = 15
   • Total students = 30 girls + 15 boys = 45 students

2. Determine the number of boys who like football.

   • Boys who like football = 10

3. Calculate the probability.

   • The probability \( P \) that a randomly selected student is a boy who likes football is given by the formula: \[ P(\text{boy who likes football}) = \frac{\text{Number of boys who like football}}{\text{Total number of students}} = \frac{10}{45} \]

4. Reduce the fraction.

   • To simplify \( \frac{10}{45} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 5: \[ \frac{10 \div 5}{45 \div 5} = \frac{2}{9} \]

Thus, the final answer for the probability that a randomly selected student will be a boy who likes football is:

\(\frac{2}{9}\)