# Question #bf95f

May 16, 2017

$p = \frac{6}{9}$ In other words, $p = \frac{2}{3}$

#### Explanation:

You have total 9 marbles. You have only 3 red marbles and 6 other colored marbles.

Now you are searching for a marble randomly picked and it is not red.

$p = \frac{6}{9}$ (only one random pick)

When you simplify,

$p = \frac{2}{3}$

or approximately 67 percent.

May 16, 2017

Answer: $\frac{2}{3}$

#### Explanation:

We have two options to solve this problem algebraically, I have listed both of them here.

Option 1:
Note that there are 6 non-red marbles and 9 total marbles, therefore the probability of selecting a non-red marble is $\frac{6}{9} = \frac{2}{3}$

Option 2:
We can use complementary counting to find the probability of which the marble drawn is not red. (Complementary counting is frequently used to find the number of ways or probability of something NOT happening.)

First, we find the probability that the marble selected IS red then subtract it from $1$, the probability that we select a marble of any color.

Since the total number of marbles in the jar is $9$ and there are $3$ red marbles, there is a $\frac{3}{9} = \frac{1}{3}$ probability of drawing a red marble.

Now, we can do $1 - \frac{1}{3} = \frac{2}{3}$, so that there is a $\frac{2}{3}$ probability of selecting a marble that is not red.