Seven White Bails And Three Black Balls Are Randomly Placed In A Row. The Probability That No Two Black Balls Are Placed Adjacently Equals

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is then,

If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers 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

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