There Are Four Machines And It Is Known That Exactly Two Of Them Are Faulty. They Are Tested, One By One, In A Random Order Till Both The Faulty Machines Are Identified. Then The Probability That Only Two Tests Are Needed Is

Let A, B, C, be three mutually independent events. Consider the two statements S₁ and S₂.

                        S₁ : A and B ∪ C are independent

                        S₂ : A and B ∩ C are independent

Then

If m is a natural such that m ≤ 5, then the probability that the quadratic that the quadratic equation x² + mx +  has real roots is

There are m persons setting in a row. Tow of then the selected at random. The probability that the two selected person are not together is

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A’) + P(B’) is

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

If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes values at most 3 is

If two events A and B such that P(A’) = 0.3, P(B) = 0.5 and P(A ∩ B) = 0.3, then  is

Seven white bails and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that two white and one black ball will be drawn is

A group of 2n boys and 2n girls is randomly divided into two equal groups. The probability that each group contains the same number of boys and girls is