Step by step
The question
Question: A bag has 3 red, 5 blue and 4 green marbles.
One marble is picked without looking.
What is the probability it is blue?
There are four choices.
First we solve it, the normal way.
Then we pick.
The probability is a fraction: the outcomes we want, over all the outcomes.
P stands for probability.
1 Count all outcomes
3 red.
5 blue.
4 green.
So there are 12 marbles in all.
3 plus 5 plus 4 is 12.
2 Count the ones we want
The blue marbles: 5.
That is 5 outcomes we want.
3 Write the fraction
5 we want, out of 12.
So the probability is 5/12.
Careful!
The bottom is all the outcomes, 12.
Not only the other 7.
4 As a percent
Percent means out of 100.
5/12 means 5 divided by 12.
Then times 100.
To the nearest tenth, that is about 41.7%.
5 Check
Let's check with the others.
12 minus 5 is 7.
5/12 plus 7/12 is 12/12: that is 1, all of them.
So the answer is right!
6 Pick the choice
Our answer is P(blue) = 5/12.
That is choice B.
7 Why not the others
A is 1/12.
Wrong: 1 out of 12: there are 5 blue marbles.
C is 5/7.
Wrong: 5 out of the 7 that are not blue: the bottom is all 12 marbles.
That is the Careful mistake from before.
D is 7/12.
Wrong: that is the chance it is not blue.
Let's look back.
First: count all outcomes.
Then: count the ones we want.
Then: write the fraction.
Then: as a percent.
Then: check.
Then: pick the choice.
Last: why not the others.