A bag has 2 red, 4 blue, 3 green and 1 yellow marbles, P(red or… Step by Step

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The question

Question: A bag has 2 red, 4 blue, 3 green and 1 yellow marbles.

One marble is picked without looking.

What is the probability it is red or yellow?

1 Find each one

Call red A.

There are 2.

A = red → 2 marbles

P stands for probability.

There are 10 outcomes in all.

P = probability, all = 10

Call yellow B.

There is 1.

B = yellow → 1 marble

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: 2/10, plus 1/10.

P(A or B) = 210 + 110

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) = 2 + 110

2 plus 1 is 3.

So it is 3/10.

P(A or B) = 310

4 Check

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

2 plus 1 is 3.

3 out of 10.

The same.

So the answer is right!

in the circles: 2 + 1 = 3 → 310

Let's look back.

First: find each one.

Then: draw a Venn diagram.

Then: add them.

Last: check.

Answer