Roll two dice, odds for doubles Step by Step

Step by step

The question

Question: Two dice are rolled.

What are the odds for getting doubles?

The odds for something compare the outcomes for it, with the outcomes against it.

odds for = for : against

For: the outcomes we want.

Against: all the others.

for = we want, against = the others

1 Count the 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.

So there are 36 outcomes in all, each just as likely.

all = 36

2 Count for and against

The outcomes we want: doubles.

6 outcomes are for.

for = 6

All the others are against: 36 minus 6 is 30.

against = 36 − 6 = 30

3 Write the odds

For, then against: 6 to 30.

odds for = 6 : 30

Careful!

Odds compare for with against.

Not with all 36.

6/36 would be a probability.

Careful: not 6 : 36 ✗

4 Simplify

Like a ratio: both 6 and 30 can be divided by 6.

odds for = (6 ÷ 6) : (30 ÷ 6)

So the odds are 1 to 5.

odds for = 1 : 5

5 Check

Let's check: for and against together are 6 plus 30, that is 36.

Every outcome is counted once.

So the answer is right!

for + against = 6 + 30 = 36 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Then: simplify.

Last: check.

Answer