A bag has 3 red, 5 blue and 2 green marbles, P(not blue) 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 not blue?

Not blue means every outcome except blue.

So we find the probability of blue first.

Then we take it from 1.

P(not blue) = 1 − P(blue)

P stands for probability.

All the outcomes together make 1.

P = probability

P(not A) = 1 − P(A)

1 Count all outcomes

So there are 10 marbles in all.

all = 10

3 plus 5 plus 2 is 10.

3 + 5 + 2 = 10

2 Find the opposite

The blue marbles: 5.

That is 5 outcomes.

blue = 5

So the probability of blue is 5/10.

P(blue) = 510

3 Take it from 1

Now we take it from 1.

P(not blue) = 1 − 510

Careful!

1 is all the outcomes: 10/10.

Careful: 1 = 1010 (all of them)

So we write 1 as 10/10.

P(not blue) = 1010 − 510

Same bottoms: we take away the tops.

10 minus 5 is 5.

P(not blue) = 510

4 Simplify

Both 5 and 10 can be divided by 5.

That makes it simpler.

P(not blue) = 5 ÷ 510 ÷ 5

So it is 1/2.

P(not blue) = 12

5 As a percent

Percent means out of 100.

We make the bottom 100: times 50, top and bottom.

50 out of 100 is 50%.

P(not blue) = 50100 = 50%

1 × 50 = 50

2 × 50 = 100

6 Check

Let's check by counting the others straight away.

5 out of 10.

The same.

So the answer is right!

not blue: 5 of 10 → 510

Let's look back.

First: count all outcomes.

Then: find the opposite.

Then: take it from 1.

Then: simplify.

Then: as a percent.

Last: check.

Answer