List of top Mathematics Questions on Bayes' Theorem asked in KEAM

Let \( A \) and \( B \) be two events. If \( P(A|B)=0.4 \), \( P(A|B')=0.7 \) and \( P(B)=0.7 \), then \( P(A) \) is

In a chess tournament, assume that your probability of winning a game is 0.3 against level 1 players, 0.4 against level 2 players and 0.5 against level 3 players. If among the players 50% are level 1, 25% are level 2 and the remaining are level 3, the probability of winning a game against a randomly chosen player is

In a chess tournament, assume that your probability of winning a game is 0.3 against level 1 players, 0.4 against level 2 players and 0.5 against level 3 players. It is further assumed that among the players 50% are at level 1, 25% are at level 2 and the remaining are at level 3. Suppose that you win the game. Then the probability that you had played with level 1 player is