Question

Suppose we want to pick two numbers from {1,2,...,100} randomly. What is the probability that the sum of the two picked numbers is divisible by 5.

Answer 1

The probability that the sum of the two picked numbers is divisible by 5 is 0.2.

Explanation:

Given;

set of numbers from {1,2,...,100}

From the set of the given numbers, we will select two numbers divisible by 5.

Using modular approach;

modulo 5 ≡ 0 are 20 -----equation (1)

modulo 5 ≡ 1 are 20 ------- equation (2)

modulo 5 ≡ 2 are 20 ------- equation (3)

modulo 5 ≡ 3 are 20 -------- equation (4)

modulo 5 ≡ 4 are 20 ---------- equation (5)

2 numbers chosen from equation (1) will be divisible by 5 OR 1 number from equation (2) and equation (5) OR 1 number from equation (3) and equation (4).

= (20C₂ + 20C₁ x 20C₁ + 20C₁ x 20C₁)

= (190 + 400 + 400)

= 990 ways

Total outcome = 100C2 = 4950

The probability of picking sum of two numbers divisible 5 = 990/4950

= 0.2