Pick a number from 1 to 30, P(multiple of 7) Step by Step

Step by step

The question

Question: A number from 1 to 30 is picked at random.

What is the probability it is a multiple of 7?

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

P(multiple of 7) = we wantall

P stands for probability.

P = probability

1 Count all outcomes

The numbers are 1 to 30.

So there are 30 outcomes.

Each one is just as likely.

all = 30

2 Count the ones we want

Multiples of 7: 7, 14, 21 and 28.

That is 4 outcomes we want.

we want = 4

3 Write the fraction

4 we want, out of 30.

So the probability is 4/30.

P(multiple of 7) = 430

Careful!

The bottom is all the outcomes, 30.

Not only the other 26.

Careful: not 426 ✗

4 Simplify

Both 4 and 30 can be divided by 2.

That makes it simpler.

P(multiple of 7) = 4 ÷ 230 ÷ 2

So it is 2/15.

P(multiple of 7) = 215

5 As a percent

Percent means out of 100.

2/15 means 2 divided by 15.

Then times 100.

To the nearest tenth, that is about 13.3%.

P(multiple of 7) ≈ 13.3%

2 ÷ 15 = 0.13333…

0.13333… × 100 ≈ 13.3%

6 Check

Let's check with the others.

30 minus 4 is 26.

4/30 plus 26/30 is 30/30: that is 1, all of them.

So the answer is right!

P(multiple of 7) + P(not multiple of 7) = 430 + 2630 = 3030 = 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