A bag has 4 red, 3 blue and 3 green marbles, P(blue or green) Step by Step

Step by step

The question

Question: A bag has 4 red, 3 blue and 3 green marbles.

One marble is picked without looking.

What is the probability it is blue or green?

1 Find each one

Call blue A.

There are 3.

A = blue → 3 marbles

P stands for probability.

There are 10 outcomes in all.

P = probability, all = 10

Call green B.

There are 3.

B = green → 3 marbles

Is anything in both?

No.

A marble has only one colour.

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: 3/10, plus 3/10.

P(A or B) = 310 + 310

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 + 310

3 plus 3 is 6.

So it is 6/10.

P(A or B) = 610

4 Simplify

Both 6 and 10 can be divided by 2.

That makes it simpler.

P(A or B) = 6 ÷ 210 ÷ 2

So it is 3/5.

P(A or B) = 35

5 Check

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

3 plus 3 is 6.

6 out of 10.

The same.

So the answer is right!

in the circles: 3 + 3 = 6 → 610

Let's look back.

First: find each one.

Then: draw a Venn diagram.

Then: add them.

Then: simplify.

Last: check.

Answer