Roll two dice, P(sum is not 7)

Step by step

The question

Question: Two dice are rolled.

What is the probability the sum is not 7?

Sum not 7 means every outcome except sum 7.

So we find the probability of sum 7 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

Sums of 7: 6 boxes.

That is 6 outcomes.

So the probability of sum 7 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.