Question

Suppose you are playing a game in which two fair dice are to rolled. To make the first move, you need to roll doubles or a sum of 3 or 11. What is the probability that you will be able make the first move?

Answer 1

`5/18 =0.278`

Explanation:

so we need the probability of

`a`= rolling doubles or `b`=sum of 3 or 11.

`p(a vv b) = p(a)+p(b)` if they are independent.

In fact rolling a double will never be a sum of 3 or 11 so these are mutually exclusive events.
Hence, the total numbers you can get is `6xx6` so no matter what you roll there are always `36` possible outcomes.

`p(a) = 6/36`, you can only roll a double for each number.

`p(b) = 4/36`, you can get a sum of 3 by rolling either a 1,2 or 2,1 and the same logic for obtaining an 11 from 5,6 or 6,5.

Putting it together by adding:

`p(a vv b) =6/36+4/36 = 10/36 = 5/18 =0.278`