Probability Questions (959)

If \(P(A) = 0.8\), \(P(B) = 0.5\), and \(P(B/A) = 0.4\), find \(P(A/B)\).

A bag contains 10 different balls. Five balls are drawn simultaneously and then replaced and then seven balls are drawn. If the probability that exactly three balls are common to the two draws is \(p\), then the value of \(8p\) is ________.

A fair coin is tossed 99 times. Let \(X\) be the number of times heads occurs. Then \(P(X = r)\) is maximum when \(r\) is

An urn is placed at vertex \(A\) of triangle \(ABC\). A ball moves from any vertex to one of the two adjacent vertices with equal probability at each step. The probability that the ball is back at vertex \(A\) after 4 steps is

Consider a game played by 10 people in which each flips a fair coin at the same time. If all but one of the coins comes up the same, then the odd person wins (e.g., if there are nine tails and one head then person having head wins). If such a situation does not occur, the players flip again. Find the probability that game is settled on or after nth toss.

Events \(A\) and \(C\) are independent. If the probabilities relating \(A\), \(B\), and \(C\) are \(P(A) = 1/5\), \(P(B) = 1/6\); \(P(A \cap C) = 1/20\); \(P(B \cup C) = 3/8\). Then

A die is thrown a fixed number of times. If probability of getting even number 3 times is same as the probability of getting even number 4 times, then probability of getting even number exactly once is

A box contains tickets numbered from 1 to 20. Three tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7 is

There are two urns \(A\) and \(B\). Urn \(A\) contains 5 red, 3 blue, and 2 white balls, urn \(B\) contains 4 red, 3 blue, and 3 white balls. An urn is chosen at random and a ball is drawn. Probability that the ball drawn is red is