Roll a die, P(less than 3) Step by Step

Step by step

The question

Question: A fair die is rolled.

What is the probability of getting a number less than 3?

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

P(less than 3) = we wantall

P stands for probability.

P = probability

1 Count all outcomes

A die has 6 sides: 1, 2, 3, 4, 5 and 6.

So there are 6 outcomes.

Each one is just as likely.

all = 6

2 Count the ones we want

Numbers less than 3: 1 and 2.

That is 2 outcomes we want.

we want = 2

3 Write the fraction

2 we want, out of 6.

So the probability is 2/6.

P(less than 3) = 26

Careful!

The bottom is all the outcomes, 6.

Not only the other 4.

Careful: not 24 ✗

4 Simplify

Both 2 and 6 can be divided by 2.

That makes it simpler.

P(less than 3) = 2 ÷ 26 ÷ 2

So it is 1/3.

P(less than 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(less than 3) ≈ 33.3%

1 ÷ 3 = 0.33333…

0.33333… × 100 ≈ 33.3%

6 Check

Let's check with the others.

6 minus 2 is 4.

2/6 plus 4/6 is 6/6: that is 1, all of them.

So the answer is right!

P(less than 3) + P(not less than 3) = 26 + 46 = 66 = 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