Question

You roll two dice. What is the probability of getting a 3 or a 6 on the second die, given that you rolled a 1 on the first die?

Answer 1

`P(3 or 6) =1/3`

Explanation:

Notice that the outcome of the first die does not affect the outcome of the second. We are only asked about the probability of a `3or 6` on the second die.

There are `63` numbers on a die, of which we want two - either `3 or 6`

`P(3 or 6) = 2/6 = 1/3`

If you are wanting the probability for both dice, then we have to consider the probability of getting the `1` first.

`P(1,3) or (1,6) = P(1,3) +P(1,6)`

`= (1/6 xx 1/6) + (1/6 xx 1/6)`

`=1/36 +1/36 = 2/36 = 1/18`

We could also have done: `1/6 xx 1/3 = 1/18`