| List-I (Sentences) | List-II (Adverbs) |
| (A) \( P(A \cap B) \) | (I) \(\frac{2}{5}\) |
| (B) \( P(A | B) \) | (II)\( \frac{4}{15}\) |
| (C) \( P(A' | B) \) | (III) \(\frac{3}{5}\) |
| (D) \( P(A' \cap B') \) | (IV) \(\frac{2}{9}\) |
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.
Three friends, P, Q, and R, are solving a puzzle with statements:
(i) If P is a knight, Q is a knave.
(ii) If Q is a knight, R is a spy.
(iii) If R is a knight, P is a knave. Knights always tell the truth, knaves always lie, and spies sometimes tell the truth. If each friend is either a knight, knave, or spy, who is the knight?