In a test with 5 options per question, a student knows the answer with probability $\frac{3}{5}$ and otherwise guesses. The student answers a question correctly. What is the probability that they knew the answer?

Explanation

1. 01

   Let $K$ be knowing the answer and $C$ answering correctly: $P(C) = \frac{3}{5} \times 1 + \frac{2}{5} \times \frac{1}{5} = \frac{17}{25}$.

2. 02

   $P(K \mid C) = \frac{3/5}{17/25} = \frac{15}{17}$.