Roll a die, odds for even Step by Step

Step by step

The question

Question: A fair die is rolled.

What are the odds for getting an even number?

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

A die has 6 sides: 1, 2, 3, 4, 5 and 6.

So there are 6 outcomes in all, each just as likely.

all = 6

2 Count for and against

The outcomes we want: even numbers.

3 outcomes are for.

for = 3

All the others are against: 6 minus 3 is 3.

against = 6 − 3 = 3

3 Write the odds

For, then against: 3 to 3.

odds for = 3 : 3

Careful!

Odds compare for with against.

Not with all 6.

3/6 would be a probability.

Careful: not 3 : 6 ✗

4 Simplify

Like a ratio: both 3 and 3 can be divided by 3.

odds for = (3 ÷ 3) : (3 ÷ 3)

So the odds are 1 to 1.

odds for = 1 : 1

5 Check

Let's check: for and against together are 3 plus 3, that is 6.

Every outcome is counted once.

So the answer is right!

for + against = 3 + 3 = 6 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Then: simplify.

Last: check.

Answer