Question

Each face of a six-sided cube is painted a different color. The cube is rolled twice and a coin is flipped. How many different possible outcomes exist?

13
24
36
72

Answer 1

D. 72

Explanation:

We have a six-sided cube that has 6 different colours. Let's say these six colours are red (R), blue (B), green (G), yellow (Y), white (W), and purple (P).

We also have a double-sided coin, which has two possible outcomes: a head (H) and a tail (T).

Each of the 6 colours can match with each of the two sides of the coin. So we can multiply 6 by 2 to get: 6 * 2 = 12.

However, note that the cube is rolled twice, which means that again, each of the 6 colours from the first roll can be paired with each of the 6 colours from the second roll, which can in turn be paired with each of the two sides of the coin.

So, multiply 12 by 6: 12 * 6 = 72.

The answer is thus D.

Answer 2

72

Explanation:

There are 6 possible outcomes for the first roll, 6 possible outcomes for the second roll, and 2 possible outcomes for the coin flip. Since all of the events are independent, you can simply multiply these together to get a total of 72 outcomes. Hope this helps!