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
