Roll a die, P(even or 5) Step by Step

Step by step

The question

Question: A fair die is rolled.

What is the probability of getting an even number or a 5?

1 Find each one

Call even A.

That is 2, 4 and 6.

A = even → 2, 4, 6

P stands for probability.

There are 6 outcomes in all.

P = probability, all = 6

Call 5 B.

That is 5.

B = 5 → 5

Is anything in both?

No.

Nothing is A and B at the same time.

A and B = nothing

2 Draw a Venn diagram

3 Add them

A or B: we add them.

Nothing is counted twice.

P(A or B) = P(A) + P(B)

When two things can't happen together, we call them mutually exclusive.

mutually exclusive:

they can't happen together

In numbers: 3/6, plus 1/6.

P(A or B) = 36 + 16

Careful!

Nothing is in both, so there is nothing to take away.

Careful: nothing in both: nothing to take away

Same bottoms: we add and take away the tops.

P(A or B) = 3 + 16

3 plus 1 is 4.

So it is 4/6.

P(A or B) = 46

4 Simplify

Both 4 and 6 can be divided by 2.

That makes it simpler.

P(A or B) = 4 ÷ 26 ÷ 2

So it is 2/3.

P(A or B) = 23

5 Check

Let's check: we count what is inside the circles.

2, 4, 5 and 6: 4.

4 out of 6.

The same.

So the answer is right!

in the circles: 2, 4, 5, 6 → 46

Let's look back.

First: find each one.

Then: draw a Venn diagram.

Then: add them.

Then: simplify.

Last: check.

Answer