In a game called “odd man out man out”, m(m > 2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is
Let A denote the event that there is an odd man out in a game. The total number of possible cases is 2m. A person is odd man out if he is alone in getting a head or a tail. The number of ways in which there is exactly one tail (head) and the rest are heads (tails) is
Thus, the number of favorable ways is m + 2m. Therefore,
In a hurdle race, a runner has probability p of jumping over a specific hurdle. Given that in 5 trials, the runner succeeded 3 times, the conditional probability that the runner had succeeded in the first trial is
Three integers are chosen at random without replacement from the first 20 integers. The probability that their product is even 2/19.
A box contains tickets numbered 1 to N. n tickets are drawn from the box with replacement. The probability that the largest number on the tickets is k is
A box contain N coins, m of which are fair and rest are biased. The probability of getting a head when a fair coin is tossed is 1/2, when a baised coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. The probability that the coin drawn is fair is
Given that A, B and C are events such that P(A) = P(B) = P(C) = 1/5, P(A∩ B) = P(B ∩ C) = 0 and P(A ∩ C) = 1=10. The probability that at least one of the events A, B or C occurs is …….
Let A and B be two events such that
A and B toss a coin alternatively till one of them gets a head and wins the game. If A begins the game, the probability B wins the game is
Suppose X ~ B(n, p) and P(X = 5). If p > 1/2, then
A person is known to speak the truth 4 time out of 5. He throws a dia and reports that it is a ace. The probability that it is actually a ace is
The chance of an event happening is the square of the chance of happening of second event but the odds against the first are the cube of the odds against the second. The chance of the events: