Question

sophie is designing a new board game, and is trying to figure out all the possible outcomes. how many different possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, flips a coin, and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?

Explanation:

Step1: Determine outcomes for pyramid die

The pyramid die has 4 sides, so there are 4 possible outcomes.

Step2: Determine outcomes for coin flip

A coin has 2 sides (heads or tails), so there are 2 possible outcomes.

Step3: Determine outcomes for cube die

The cube die has 6 sides, so there are 6 possible outcomes.

Step4: Calculate total outcomes using multiplication principle

To find the total number of possible outcomes when performing multiple independent events, we multiply the number of outcomes for each event. So we multiply the number of outcomes for the pyramid die, coin flip, and cube die: $4\times2\times6$.
First, calculate $4\times2 = 8$. Then, calculate $8\times6 = 48$.

Answer:

48