Roll two dice, P(sum is 8) Step by Step

Step by step

The question

Question: Two dice are rolled.

What is the probability the sum is 8?

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

P(sum 8) = we wantall

P stands for probability.

P = 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.

all = 6 × 6 = 36

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

sample space = all the outcomes

2 Count the ones we want

Sums of 8: 5 boxes.

That is 5 outcomes we want.

we want = 5

3 Write the fraction

5 we want, out of 36.

So the probability is 5/36.

P(sum 8) = 536

Careful!

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

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

Careful: not 111 ✗

4 Check

Let's check with the others.

36 minus 5 is 31.

5/36 plus 31/36 is 36/36: that is 1, all of them.

So the answer is right!

P(sum 8) + P(not sum 8) = 536 + 3136 = 3636 = 1

Let's look back.

First: list all outcomes.

Then: count the ones we want.

Then: write the fraction.

Last: check.

Answer