Question

What is the probability that a positive integers selected randomly from the set of positive itegers ot exceedig 100 is divisile y 3 or 4

Answer 1

Hint The largest multiple of 33 in {1,…,1000}{1,…,1000} is 3⌊10003⌋=3⋅333=9993⌊10003⌋=3⋅333=999 and so there are ⌊10003⌋=333⌊10003⌋=333 mutiples of 33 in that range. Similarly, there are ⌊10005⌋=200⌊10005⌋=200multiples of 55, and there are ⌊100015⌋=66⌊100015⌋=66 multiples of 3⋅5=153⋅5=15.