Roll a die, P(1 or 6) Step by Step

Step by step

The question

Question: A fair die is rolled.

What is the probability of getting a 1 or a 6?

1 Find each one

Call 1 A.

That is 1.

A = 1 → 1

P stands for probability.

There are 6 outcomes in all.

P = probability, all = 6

Call 6 B.

That is 6.

B = 6 → 6

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: 1/6, plus 1/6.

P(A or B) = 16 + 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) = 1 + 16

1 plus 1 is 2.

So it is 2/6.

P(A or B) = 26

4 Simplify

Both 2 and 6 can be divided by 2.

That makes it simpler.

P(A or B) = 2 ÷ 26 ÷ 2

So it is 1/3.

P(A or B) = 13

5 Check

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

1 and 6: 2.

2 out of 6.

The same.

So the answer is right!

in the circles: 1, 6 → 26

Let's look back.

First: find each one.

Then: draw a Venn diagram.

Then: add them.

Then: simplify.

Last: check.

Answer