Pick a number from 1 to 10, P(even) Step by Step

Step by step

The question

Question: A number from 1 to 10 is picked at random.

What is the probability it is 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

The numbers are 1 to 10.

So there are 10 outcomes.

Each one is just as likely.

all = 10

2 Count the ones we want

Even numbers: 2, 4, 6, 8 and 10.

That is 5 outcomes we want.

we want = 5

3 Write the fraction

5 we want, out of 10.

So the probability is 5/10.

P(even) = 510

4 Simplify

Both 5 and 10 can be divided by 5.

That makes it simpler.

P(even) = 5 ÷ 510 ÷ 5

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.

10 minus 5 is 5.

5/10 plus 5/10 is 10/10: that is 1, all of them.

So the answer is right!

P(even) + P(not even) = 510 + 510 = 1010 = 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