Roll two dice, P(not doubles)

Step by step

The question

Question: Two dice are rolled.

What is the probability of not getting doubles?

Not doubles means every outcome except doubles.

So we find the probability of doubles first.

Then we take it from 1.

P stands for probability.

All the outcomes together make 1.

1 List all outcomes

The first die goes across.

The second die goes down.

Each box is one outcome.

We write the sum of the two dice in it.

6 times 6 is 36 outcomes, all just as likely.

This list of all the outcomes is called the sample space.

2 Find the opposite

Doubles: 6 boxes.

That is 6 outcomes.

So the probability of doubles is 6/36.

3 Take it from 1

Now we take it from 1.

Careful!

1 is all the outcomes: 36/36.

So we write 1 as 36/36.

Same bottoms: we take away the tops.

36 minus 6 is 30.

4 Simplify

Both 30 and 36 can be divided by 6.

That makes it simpler.

So it is 5/6.

5 Check

Let's check by counting the others straight away.

30 out of 36.

The same.

So the answer is right!

Let's look back.

First: list all outcomes.

Then: find the opposite.

Then: take it from 1.

Then: simplify.

Last: check.