Roll two dice, odds against sum is 7 Step by Step

Step by step

The question

Question: Two dice are rolled.

What are the odds against the sum being 7?

The odds against something put the outcomes against it first, then the outcomes for it.

odds against = against : for

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: sums of 7.

6 outcomes are for.

for = 6

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

against = 36 − 6 = 30

3 Write the odds

Against, then for: 30 to 6.

odds against = 30 : 6

Careful!

Odds compare against with for.

Not with all 36.

30/36 would be a probability.

Careful: not 30 : 36 ✗

4 Simplify

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

odds against = (30 ÷ 6) : (6 ÷ 6)

So the odds are 5 to 1.

odds against = 5 : 1

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