# A cube has six sides that are numbered 1 to 6. The sides numbered 1, 2, and 5 are green, and the sides numbered 3, 4, and 6 are red. What is the probability of rolling the cube and getting a green or even number?

May 17, 2018

See explanation.

#### Explanation:

In the task we have the following events:

$G$ - choosing a green side

$E$ - choosing a side with an even number

$G \cap E$ - choosing a side which is green and has an even number

$G \cup E$ - - choosing a side which is green or has an even number

The probabiliyies are:

$P \left(G\right) = \frac{3}{6} = \frac{1}{2}$ (there are $3$ green sides)

$P \left(E\right) = \frac{3}{6} = \frac{1}{2}$ (there are $3$ sides with an even number)

$P \left(G \cap E\right) = \frac{1}{6}$ (there is one green side with an even number: $2$)

Now to calculate the probability of the sum of events we use the formula:

$P \left(G \cup E\right) = P \left(G\right) + P \left(E\right) - P \left(E \cap G\right)$

If we do the calculation we get:

$P \left(G \cup E\right) = \frac{1}{2} + \frac{1}{2} - \frac{1}{6} = 1 - \frac{1}{6} = \frac{5}{6}$