Pick a number from 1 to 12, P(multiple of 3) Step by Step

Step by step

The question

Question: A number from 1 to 12 is picked at random.

What is the probability it is a multiple of 3?

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

P(multiple of 3) = we wantall

P stands for probability.

P = probability

1 Count all outcomes

The numbers are 1 to 12.

So there are 12 outcomes.

Each one is just as likely.

all = 12

2 Count the ones we want

Multiples of 3: 3, 6, 9 and 12.

That is 4 outcomes we want.

we want = 4

3 Write the fraction

4 we want, out of 12.

So the probability is 4/12.

P(multiple of 3) = 412

Careful!

The bottom is all the outcomes, 12.

Not only the other 8.

Careful: not 48 ✗

4 Simplify

Both 4 and 12 can be divided by 4.

That makes it simpler.

P(multiple of 3) = 4 ÷ 412 ÷ 4

So it is 1/3.

P(multiple of 3) = 13

5 As a percent

Percent means out of 100.

1/3 means 1 divided by 3.

Then times 100.

To the nearest tenth, that is about 33.3%.

P(multiple of 3) ≈ 33.3%

1 ÷ 3 = 0.33333…

0.33333… × 100 ≈ 33.3%

6 Check

Let's check with the others.

12 minus 4 is 8.

4/12 plus 8/12 is 12/12: that is 1, all of them.

So the answer is right!

P(multiple of 3) + P(not multiple of 3) = 412 + 812 = 1212 = 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