Two numbers a and b chosen at random from the set of first 30 natural numbers. Find the probability that `a^(2) - b^(2)` is divisible by 3.

Two number aa n db aer chosen at random from the set of first 30 natural numbers. Find the probability that a^2-b^2 is divisible by 3.

If two distinct numbers m and n are chosen at random form the set {1, 2, 3, …, 100}, then find the probability that 2^(m) + 2^(n) + 1 is divisible by 3.

The S.D for the set of the first 'n' natural numbers is

If three distinct number are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is (a) 4/25 (b) 4/35 (c) 4/33 (d) 4/1155

Two natural numbers x and y are chosen at random. What is the probability that x^(2) + y^(2) is divisible by 5?

An integer is chosen at random from the first 20 positive integers.Find the probability that it (i)An even number (ii)Divisible by 5 (iii)A prime number.

A natural number is chosen at random from the first 100 natural numbers. The probability that x+(100)/x > 50 is 1//10 b. 11//50 c. 11//20 d. none of these

Two numbers x and y are chosen at random (without replacement) from among the numbers 1,2,3,2004. The probability that x^3+y^3 is divisible by 3 is (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/4

Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is 194//285 b. 1//57 c. 13//19 d. 3//4