A natural number x is chosen at random from the first one hundred natural numbers. The probability that   is


Correct option is


Sign of E is same as that of sign of   

               (x – 20) (x – 30) (x – 40) = F(say). 

Note that F < 0 if and only if

               0 < x < 20 or 30 < x < 40.

∴              E < 0 in (0, 20) ∪ (30, 40)

Thus, E is negative for x = 1, 2,….,19, 31, 32,….,39, that is E, < 0 for 28 nature numbers.

∴   Required probability = 28/100 = 7/25.



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


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


Let A and B be two events such that P(A) = 0.3 and P(A  B) = 0.8. If Aand B are independent events, then P(B) is


An unbiased dia with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times out of the four faces obtained, the probability that the minimum value is exactly than 2 and the maximum value is exactly 5 is


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


Each of two persons A and B toss three fair coins. The probability that both get the same number of heads is


The probability that a student is not a swimmer is 1/5. The probability that out of 5 students exactly 4 is swimmer is


Six distinct numbers are selected from first 150 natural numbers. The probability all the six numbers are divisible both by 3 and 5 is


There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is


An experiment has 10 equally likely outcomes. Let A and B two non – empty events of the experiment. If a consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is