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?

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Answer 1 · 2018-05-17T17:50:22

See explanation.

In the task we have the following events:

$G$ - choosing a green side

$E$ - choosing a side with an even number

$GnnE$ - choosing a side which is green and has an even number

$GuuE$ - - choosing a side which is green or has an even number

The probabiliyies are:

$P(G)=3/6=1/2$ (there are $3$ green sides)

$P(E)=3/6=1/2$ (there are $3$ sides with an even number)

$P(GnnE)=1/6$ (there is one green side with an even number: $2$ )

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

$P(GuuE)=P(G)+P(E)-P(EnnG)$

If we do the calculation we get:

$P(GuuE)=1/2+1/2-1/6=1-1/6=5/6$