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 **
Given:
$P(\text{Physics fail}) = 0.30$
$P(\text{Math fail}) = 0.25$
$P(\text{Fail both}) = 0.10$
We need: $P(\text{Physics fail} \mid \text{Math fail})$
Use conditional probability:
$P(\text{Physics fail} \mid \text{Math fail}) = \frac{P(\text{Fail both})}{P(\text{Math fail})}$
$= \frac{0.10}{0.25}$
$= 0.40$
The required probability is $0.40$.