# A box contains 5 red, 2 white, & 3 blue marbles. If a marble is selected at random, what is the probability that it is not red?

$\frac{5}{10}$

#### Explanation:

We have a box with 10 marbles: 5 Red, 2 White, 3 Blue.

The probability of picking any one marble at random is $\frac{1}{10}$ - i.e. that one marble out of ten choices.

We're asked for the probability that the marble we pick at random isn't red. So let's do this in two ways:

Direct calculation of non-red marbles

There are 5 marbles that are not red: 2 white and 3 blue. There are, therefore, 5 marbles out of the 10 that aren't red, so the probability of picking either a white or blue marble (and therefore not a red one) is:

$\frac{2}{10} + \frac{3}{10} = \frac{5}{10}$

Indirect calculation of non-red marbles

We can see that there are 5 red marbles out of the total marble count of 10. Therefore, we can deduct the chance of getting a red marble from the sum of all choices (100%) and calculate the chance of getting a non-red marble:

$\frac{10}{10} - \frac{5}{10} = \frac{5}{10}$