Probability
Probability
star_batch_jee_advanced_2025
Grade 12
Question:
Rajesh doesn't like to study. Probability that he will study is $1/3$. If he studied, then probability that he will fail is $1/2$ and if he didn't study then probability that he will fail is $3/4$. If in result Rajesh failed, then what is the probability that he didn't study.
Step-by-Step Solution
Key Concept: Apply the law of total probability first to find the total probability of failure, then use Bayes' theorem for conditional probability.
The candidate fails in two cases: (i) studied and failed with probability $(1/3)(1/2) = 1/6$; (ii) didn't study and failed with probability $(2/3)(3/4) = 1/2$. Total probability of failure is $1/6 + 1/2 = 2/3$. Using Bayes' theorem, probability of not studying given failure is $(1/2)/(2/3) = 3/4$.
Correct Answer: 0.75