In an examination involving multiple choice questions, a student works out the solution in 50% of the questions. In the remaining questions the student guesses the answer. However, when the answer is guessed the probability that it is correct is 0.30. When the student works out the solutions it may be wrong with probability 0.10.

If the answer to a particular question is correct, what is the probability that the student guessed the answer?

Explanation:

Let

W: student works out the solution.

G: student guess the answer

C: answer is correct

D: answer is not correct.

From the given condition

P(W) = 1/2 = 0.5

P(G) = 1/2 = 0.5

P(C / G) = 0.30

P(C /  W) = 0.90

So total probability = P(W) . P(C / W) + P(G) . P(C / G) = 0.5 × 0.90 + 0.5 × 0.30 = 0.45 + 0.15 = 0.6

Hence using Baye's theorem

If the answer to a particular question is correct, then the probability that the student guessed the answer

 = P(G / C) =  \(\frac{0.5\times 0.30}{0.6}\) =0.25

Option (1) is correct.