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:

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

Step-by-step 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

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