Question

Tom rolls 2 fair dice and adds the results from each.

Work out the probability of getting a total of 4.

Answer 1

`(1)/(12)`

Explanation:

All possible outcomes:

`\begin{array}{cccccc}1,1&1,2&1,3&1,4&1,5&1,6\\2,1&2,2&2,3&2,4&2,5&2,6\\3,1&3,2&3,3&3,4&3,5&3,6\\4,1&4,2&4,3&4,4&4,5&4,6\\5,1&5,2&5,3&5,4&5,5&5,6\\6,1&6,2&6,3&6,4&6,5&6,6\end{array}`

Here, the first number is the number on the 1st die and the second number is the number on the 2nd die.

There are 36 possible outcomes.

A total of 4 give outcomes:

`1,3\\2,2\\3,1`

So, there are 3 favorable outcomes.

The probability of getting a total of 4 is

`(3)/(36)=(1)/(12)`