Pick a number from 1 to 25, P(not multiple of 5)

Step by step

The question

Question: A number from 1 to 25 is picked at random.

What is the probability it is not a multiple of 5?

Not multiple of 5 means every outcome except multiple of 5.

So we find the probability of multiple of 5 first.

Then we take it from 1.

P stands for probability.

All the outcomes together make 1.

1 Count all outcomes

The numbers are 1 to 25.

So there are 25 outcomes.

Each one is just as likely.

2 Find the opposite

Multiples of 5: 5, 10, 15, 20 and 25.

That is 5 outcomes.

So the probability of multiple of 5 is 5/25.

3 Take it from 1

Now we take it from 1.

Careful!

1 is all the outcomes: 25/25.

So we write 1 as 25/25.

Same bottoms: we take away the tops.

25 minus 5 is 20.

4 Simplify

Both 20 and 25 can be divided by 5.

That makes it simpler.

So it is 4/5.

5 As a percent

Percent means out of 100.

We make the bottom 100: times 20, top and bottom.

80 out of 100 is 80%.

6 Check

Let's check by counting the others straight away.

20 out of 25.

The same.

So the answer is right!

Let's look back.

First: count all outcomes.

Then: find the opposite.

Then: take it from 1.

Then: simplify.

Then: as a percent.

Last: check.