Roll a die, P(even) Step by Step

Step by step

The question

Question: A fair die is rolled.

What is the probability of getting an even number?

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

P(even) = 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

Even numbers: 2, 4 and 6.

That is 3 outcomes we want.

we want = 3

3 Write the fraction

3 we want, out of 6.

So the probability is 3/6.

P(even) = 36

4 Simplify

Both 3 and 6 can be divided by 3.

That makes it simpler.

P(even) = 3 ÷ 36 ÷ 3

So it is 1/2.

P(even) = 12

5 As a percent

Percent means out of 100.

We make the bottom 100: times 50, top and bottom.

50 out of 100 is 50%.

P(even) = 50100 = 50%

1 × 50 = 50

2 × 50 = 100

6 Check

Let's check with the others.

6 minus 3 is 3.

3/6 plus 3/6 is 6/6: that is 1, all of them.

So the answer is right!

P(even) + P(not even) = 36 + 36 = 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