Pick a number from 1 to 20, odds against multiple of 4 Step by Step

Step by step

The question

Question: A number from 1 to 20 is picked at random.

What are the odds against it being a multiple of 4?

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 numbers are 1 to 20.

So there are 20 outcomes in all, each just as likely.

all = 20

2 Count for and against

The outcomes we want: multiples of 4.

5 outcomes are for.

for = 5

All the others are against: 20 minus 5 is 15.

against = 20 − 5 = 15

3 Write the odds

Against, then for: 15 to 5.

odds against = 15 : 5

Careful!

Odds compare against with for.

Not with all 20.

15/20 would be a probability.

Careful: not 15 : 20 ✗

4 Simplify

Like a ratio: both 15 and 5 can be divided by 5.

odds against = (15 ÷ 5) : (5 ÷ 5)

So the odds are 3 to 1.

odds against = 3 : 1

5 Check

Let's check: for and against together are 5 plus 15, that is 20.

Every outcome is counted once.

So the answer is right!

for + against = 5 + 15 = 20 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Then: simplify.

Last: check.

Answer