A bag has 3 red, 5 blue and 2 green marbles, P(red or green) Step by Step

Step by step

The question

Question: A bag has 3 red, 5 blue and 2 green marbles.

One marble is picked without looking.

What is the probability it is red or green?

1 Find each one

Call red A.

There are 3.

A = red → 3 marbles

P stands for probability.

There are 10 outcomes in all.

P = probability, all = 10

Call green B.

There are 2.

B = green → 2 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 2/10.

P(A or B) = 310 + 210

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 + 210

3 plus 2 is 5.

So it is 5/10.

P(A or B) = 510

4 Simplify

Both 5 and 10 can be divided by 5.

That makes it simpler.

P(A or B) = 5 ÷ 510 ÷ 5

So it is 1/2.

P(A or B) = 12

5 Check

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

3 plus 2 is 5.

5 out of 10.

The same.

So the answer is right!

in the circles: 3 + 2 = 5 → 510

Let's look back.

First: find each one.

Then: draw a Venn diagram.

Then: add them.

Then: simplify.

Last: check.

Answer