Question

Two fair dice are thrown,what is the probability of getting two odd numbers?

Answer 1

`1/4`

Explanation:

The two dice are independent, i.e. the result of one die does not infuence the result of the other.

In this case, the probability of a complex event is the product of the probabilities of the simple events.

For every die, there are `3` odd outcomes and `3` even outcomes. So, the probability of getting an odd number is `3/6=1/2`

So, the probability that this happens with both dice is `1/2*1/2=1/4`

In this case, it is actually easy to enumerate the "good" outcomes: there are `36` outcomes in total (all numbers from `1` to `6` for one die and the same for the other die). The good outcomes are

`(1,1)`, `(1,3)`, `(1,5)`

`(3,1)`, `(3,3)`, `(3,5)`

`(5,1)`, `(5,3)`, `(5,5)`

And in fact, `9` good outcomes over `36` total outcomes means

`9/36 = 1/4`