Given, Sample space is the set of first 500 natural numbers.

∴ n(S) = 500

Let A be the event of choosing the number such that it is divisible by 3

∴ n(A) = [500/3] = [166.67] = 166 {where [.] represents Greatest integer function}

∴ P(A) =

Let B be the event of choosing the number such that it is divisible by 5

∴ n(B) = [500/5] = [100] = 100 {where [.] represents Greatest integer function}

∴ P(B) =

We need to find the P(such that number chosen is divisible by 3 or 5)

∵ P(A or B) = P(A ∪ B)

Note: By definition of P(E or F) under axiomatic approach(also called addition theorem) we know that:

P(E ∪ F) = P(E) + P(F) – P(E ∩ F)

∴ P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

We don’t have value of P(A ∩ B) which represents event of choosing a number such that it is divisible by both 3 and 5 or we can say that it is divisible by 15.

n(A ∩ B) = [500/15] = [33.34] = 33

∴ P(A ∩ B) =

∴ P(A ∪ B) =