Question

Two numbers a and b are chosen at random from the set of first 30 natural numbers. The probability that a² – b² is divisible by 3 is

• A. 9/87
• B. 12/87
• C. 15/87
• D. 47/87

Answer 1

Answer: (D)

47/87

Answer 2

The total number of ways of choosing two numbers out of 1, 2, 3, ..., 30 is $30C_{2} = 435$.

Since a² – b² is divisible by 3 if either a and b both are divisible by 3 or none of a and b is divisible by 3. Thus the favourable number of cases = $10C_{2} +^{20}C_{2} = 235$.

Hence the required probability = $\frac{235}{435} = \frac{47}{87}$