In a class of 30 students, 14 like mathematics, 12 like physics, and 5 like both subjects. A student is selected at random. Find the probability that the student likes mathematics given that the student likes physics.

Step-by-step solution

1. Identify the total number of students: $30$.
2. Find the number of students who like physics: $12$ (including those who like both). This is $P(Physics)=\frac{12}{30}$.
3. Find the number of students who like both mathematics and physics: $5$. This is $P(Math\cap Physics)=\frac{5}{30}$.
4. Use the definition of conditional probability: $P(Math|Physics)=\frac{P(Math\cap Physics)}{P(Physics)}$.
5. Substitute the fractions: $\frac{\frac{5}{30}}{\frac{12}{30}}=\frac{5}{12}$.

Concept tested: Conditional probability

Published 28 September 2026 · How this solution was prepared and checked

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