# A bag contains 7 red marbles, 12 orange marbles, 18 yellow marbles, and 5 purple marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be orange?

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7
Mar 17, 2017

$\frac{5}{7}$

#### Explanation:

There are 42 marbles in the bag.
When one marble is taken out at random, in terms of orange, there are only two possible outcomes:
either the marble IS orange, or it ISN'T.

There are 12 marbles which ARE orange, which means that the rest are NOT orange. $\left(42 - 12 = 30\right)$

$P \left(\text{not orange}\right) = \frac{30}{42} = \frac{5}{7}$

This can also be shown as;

$P \left(\text{an event NOT occurring") = 1 - P("DOES occur}\right)$

$P \left(\text{orange}\right) = \frac{12}{42} = \frac{2}{7}$

$P \left(\text{not orange}\right) = 1 - \frac{2}{7} = \frac{5}{7}$

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