Pick a number from 1 to 20, P(multiple of 4) Step by Step

Step by step

The question

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

What is the probability it is a multiple of 4?

The probability is a fraction: the outcomes we want, over all the outcomes.

P(multiple of 4) = we wantall

P stands for probability.

P = probability

1 Count all outcomes

The numbers are 1 to 20.

So there are 20 outcomes.

Each one is just as likely.

all = 20

2 Count the ones we want

Multiples of 4: 4, 8, 12, 16 and 20.

That is 5 outcomes we want.

we want = 5

3 Write the fraction

5 we want, out of 20.

So the probability is 5/20.

P(multiple of 4) = 520

Careful!

The bottom is all the outcomes, 20.

Not only the other 15.

Careful: not 515 ✗

4 Simplify

Both 5 and 20 can be divided by 5.

That makes it simpler.

P(multiple of 4) = 5 ÷ 520 ÷ 5

So it is 1/4.

P(multiple of 4) = 14

5 As a percent

Percent means out of 100.

We make the bottom 100: times 25, top and bottom.

25 out of 100 is 25%.

P(multiple of 4) = 25100 = 25%

1 × 25 = 25

4 × 25 = 100

6 Check

Let's check with the others.

20 minus 5 is 15.

5/20 plus 15/20 is 20/20: that is 1, all of them.

So the answer is right!

P(multiple of 4) + P(not multiple of 4) = 520 + 1520 = 2020 = 1

Let's look back.

First: count all outcomes.

Then: count the ones we want.

Then: write the fraction.

Then: simplify.

Then: as a percent.

Last: check.

Answer