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


Correct option is

Let E1E2 and A denote the following events:

     E1: coin selected is fair

     E2: coin selected is baised

      A: the first toss results in a head and the second toss results in a tail.



By Bayes’ rule




An experiment has 10 equally likely outcomes. Let A and B two non – empty events of the experiment. If a consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is


If AB and C are the events such that P(B) = 3/4, P(A ∩ B ∩ C’) = 1/3P(A’ ∩ B ∩ C’) = 1/3, then P (B ∩ C) is equal to


A fair coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that occurs 8 times, then value of n is


A person writes 4 letters and addresses on 4 envelopes. If the letters are placed in the envelopes at random, the probability that not all letters are placed in correct envelopes is


A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CACUTTA is


A group of 6 boys and 6 girls is randomly divided into two equal groups. The probability that each group contains 3 boys and 3 girls is


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 Nn tickets are drawn from the box with replacement. The probability that the largest number on the tickets is is


Given that AB 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 AB or C occurs is …….