# Math Help - Probability and divisibility

1. ## Probability and divisibility

What is the probability of not choosing a number divisible by both 4 and 3?

2. If a number is divisible by both 4 and 3, then, since 3 and 4 are relatively prime, it must be divisible by 12.

Technically, since natural numbers and multiples of 12 are both countably infinite sets, the probability of choosing a multiple of 12 is undefined. However, if there is a high upper limit on the numbers we can choose, the probability would become approximately $\frac{1}{12}$.

3. numbers 1-50

4. In that case, the numbers divisible by 12 are,

{12, 24, 36, 48}.

That leaves 50 - 4 = 46 numbers not divisible by 3 and 4.