In a college, 30% students fail in physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2/5
Let A be the event that the student fails in physics and B the event that she fails in mathematics:
\(P(A) = 0.30,\quad P(B) = 0.25,\quad P(A\cap B) = 0.10\)
The required probability is the conditional probability of A given B:
\( \displaystyle P(A|B) = \frac{P(A\cap B)}{P(B)} \)
\( \displaystyle = \frac{0.10}{0.25} = \frac{2}{5} \)
NCERT Exemplar:
Probability
