Roll a die, odds for more than 4 Step by Step

Step by step

The question

Question: A fair die is rolled.

What are the odds for getting a number more than 4?

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: numbers more than 4.

2 outcomes are for.

for = 2

All the others are against: 6 minus 2 is 4.

against = 6 − 2 = 4

3 Write the odds

For, then against: 2 to 4.

odds for = 2 : 4

Careful!

Odds compare for with against.

Not with all 6.

2/6 would be a probability.

Careful: not 2 : 6 ✗

4 Simplify

Like a ratio: both 2 and 4 can be divided by 2.

odds for = (2 ÷ 2) : (4 ÷ 2)

So the odds are 1 to 2.

odds for = 1 : 2

5 Check

Let's check: for and against together are 2 plus 4, that is 6.

Every outcome is counted once.

So the answer is right!

for + against = 2 + 4 = 6 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Then: simplify.

Last: check.

Answer