Roll two dice, P(sum more than 3)

Step by step

The question

Question: Two dice are rolled.

What is the probability the sum is more than 3?

The probability is a fraction: the outcomes we want, over all the outcomes.

P stands for probability.

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 Count the ones we want

Sums more than 3: 33 boxes.

That is 33 outcomes we want.

3 Write the fraction

33 we want, out of 36.

So the probability is 33/36.

Careful!

The 11 sums, 2 to 12, are not equally likely.

7 comes 6 ways, but 2 comes only 1 way.

4 Simplify

Both 33 and 36 can be divided by 3.

That makes it simpler.

So it is 11/12.

5 Check

Let's check with the others.

36 minus 33 is 3.

33/36 plus 3/36 is 36/36: that is 1, all of them.

So the answer is right!

Let's look back.

First: list all outcomes.

Then: count the ones we want.

Then: write the fraction.

Then: simplify.

Last: check.