Suppose we want to pick two numbers from {1,2……,100} randomly .
// means that we have to select two numbers at one go and there is no point for replacement...
sum of the two numbers is divisible by 5.
// from the set of 100 we need to select 2 numbers {{5,10}{1,9}{6,9}..........}}
20 modulo 5≡0 are 20...........@1
20 modulo 5≡1 are 20..........@2
20 modulo 5≡2 are 20...........@3
20 modulo 5≡3 are 20............@4
20 modulo 5=4 are 20............@5
=select any two numbers from @1 or select one number from @2 and other from set @5 or one from @3 and other from @4
= (20C2 + 20C1 *20C1 + 20C1 *20C1) = 990 ways
sample space = selecting 2 numbers from 100 numbers
in 100C2.
probability = 990/ 100C2 = 990/50*99=1/5 = 0.2 answer .