Probability Tes...

Three six faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k (3 ≤ k ≤ 8), is

Out of 21 tickets marked with numbers from 1 to 21, three are drawn at random. The chance that the numbers on then are in AP is

Three squares of a chess board the chosen at random, the probability that two are of one color and one of another is

A five digit number id formed by writing the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then, the probability that the number is divisible by 4 is

If a party of n persons sit at a round table, then the odds against two specified individuals sitting next to each other are

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, the probability that the light will not green is

A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then the probability that 5 comes before 7 is

Two dice are thrown simultaneously. The probability that sum is odd or less than 7 or both is

A student appears for test I, II and III. The student is successful is he passes either in test I and II or test I and III. The probabilities of the student passing in test I, II, III are p, q and 1/2 respectively. If the probability that the student is successful is 1/2, then

For the three events A, B and C, P (exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p², where 0 < p < 1/2. Then the probability of at least one of the three events A, B and C occurring is