Roll a die, P(not 6) Step by Step

Step by step

The question

Question: A fair die is rolled.

What is the probability of not getting a 6?

Not 6 means every outcome except 6.

So we find the probability of 6 first.

Then we take it from 1.

P(not 6) = 1 − P(6)

P stands for probability.

All the outcomes together make 1.

P = probability

P(not A) = 1 − P(A)

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 Find the opposite

The 6: just one.

That is 1 outcome.

6 = 1

So the probability of 6 is 1/6.

P(6) = 16

3 Take it from 1

Now we take it from 1.

P(not 6) = 1 − 16

Careful!

1 is all the outcomes: 6/6.

Careful: 1 = 66 (all of them)

So we write 1 as 6/6.

P(not 6) = 66 − 16

Same bottoms: we take away the tops.

6 minus 1 is 5.

P(not 6) = 56

4 As a percent

Percent means out of 100.

5/6 means 5 divided by 6.

Then times 100.

To the nearest tenth, that is about 83.3%.

P(not 6) ≈ 83.3%

5 ÷ 6 = 0.83333…

0.83333… × 100 ≈ 83.3%

5 Check

Let's check by counting the others straight away.

5 out of 6.

The same.

So the answer is right!

not 6: 5 of 6 → 56

Let's look back.

First: count all outcomes.

Then: find the opposite.

Then: take it from 1.

Then: as a percent.

Last: check.

Answer