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


Correct option is


Discriminate D of the quadratic equation


Is given by



Now,      D ≥ 0    ⇔         (m – 1)2 ≥ 3

This is possible for m = 3, 4 and 5. Also, the total number of ways of choosing m is 5.

∴ Probability of the required event = 3/5



A fair coin is tossed 100 times. The probability of getting tails an odd number of times is


One hundred identical coins, each with probability of head are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is


Suppose X follows a binomial distribution with parameters n and p, where 0 < p < 1. If P (X = r)/P(X = n – r) is independent of n for every value ofr, then 


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 AB and CP(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 AB 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 ABC, 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



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