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

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is

For the three events A, B and C, P(exactly one of the events A or Boccurs) = 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

Nine identical balls are numbers 1, 2,…9. Are put in a bag. A draws a ball and gets the number a. the ball is put back the beg. Next B draws a ball gets the number b. The probability that a and b satisfies the inequality a – 2b + 10 > 0 is

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

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