We know that for two independent events occurring simultaneously the probability formula is $P(A \,\text{and}\, B)= P(A) \, P(B)$, which is the Multiplication Rule. But does it work in these cases?
i) Find the probability of numbers divisible by $3$ or $5$ in a random selection from $1$ to $20$.
With the multiplying rule, it should be,
$P(\text{divisible by}\, 3) + P(\text{divisible by}\, 5) - P(A \,\text{and}\, B)$
Which is $6/20 + 4/20 - (6/20 \times 4/20) = 11/25$. But it doesn't work!! Why!?