A bag has 4 red, 6 blue and 2 green marbles, P(blue) Step by Step

Step by step

The question

Question: A bag has 4 red, 6 blue and 2 green marbles.

One marble is picked without looking.

What is the probability it is blue?

The probability is a fraction: the outcomes we want, over all the outcomes.

P(blue) = we wantall

P stands for probability.

P = probability

1 Count all outcomes

So there are 12 marbles in all.

all = 12

4 plus 6 plus 2 is 12.

4 + 6 + 2 = 12

2 Count the ones we want

The blue marbles: 6.

That is 6 outcomes we want.

we want = 6

3 Write the fraction

6 we want, out of 12.

So the probability is 6/12.

P(blue) = 612

4 Simplify

Both 6 and 12 can be divided by 6.

That makes it simpler.

P(blue) = 6 ÷ 612 ÷ 6

So it is 1/2.

P(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(blue) = 50100 = 50%

1 × 50 = 50

2 × 50 = 100

6 Check

Let's check with the others.

12 minus 6 is 6.

6/12 plus 6/12 is 12/12: that is 1, all of them.

So the answer is right!

P(blue) + P(not blue) = 612 + 612 = 1212 = 1

Let's look back.

First: count all outcomes.

Then: count the ones we want.

Then: write the fraction.

Then: simplify.

Then: as a percent.

Last: check.

Answer