Question

In a class, 40% of students study maths and science and 60% of students study maths. What is the probability of a student studying science given the student is already studying maths?

• A. \( \frac{1}{3} \)
• B. \( \frac{1}{6} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{1}{5} \)
• E. \( \frac{1}{4} \)

Hint:

Conditional probability focuses only on the reduced sample space.

Answer 1

The Correct Option is C

Concept: Conditional probability: \[ P(S|M) = \frac{P(S \cap M)}{P(M)} \]

Step 1: Interpret given data carefully.
40% students study both maths and science: \[ P(S \cap M) = 0.4 \] 60% students study maths: \[ P(M) = 0.6 \]

Step 2: Write formula for conditional probability.
\[ P(S|M) = \frac{P(S \cap M)}{P(M)} \]

Step 3: Substitute values into formula.
\[ P(S|M) = \frac{0.4}{0.6} \]

Step 4: Simplify fraction step-by-step.
\[ \frac{0.4}{0.6} = \frac{4}{6} = \frac{2}{3} \]

Step 5: Interpret result.
This means among students who study maths, \( \frac{2}{3} \) also study science.