Question

A number cube is labeled 1 through 6. What is the probability of rolling a number that is divisible by 3?

Answer 1

The probability is `P(A)=1/3`

Explanation:

To calculate the probability you have to count the number of all possible results `|Omega|` and the number of results that fulfill the given condition `|A|`.

In this case `Omega={1,2,3,4,5,6}` Thereare 6 possible result of a dice toss. So `|Omega|=6`

The given condition is "the result is divisible by `3`", so
`A={3,6}` - those are the only numbers divisible by `3`, so `|A|=2`.

Finally to calculate the probability we have to divide `|A|` by `|Omega|`.

`P(A)=(|A|)/(|Omega|)=2/6=1/3`

Note The probability is never larger than `1`, so if you get such result then there must be a mistake in calculations.