Question

kadeem is designing a new board game, and is trying to figure out all the possible outcomes. how many different possible outcomes are there if he spins a spinner with three equal - sized sections labeled walk, run, stop, rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, and flips a coin?

Explanation:

Step1: Determine outcomes for spinner

The spinner has 3 equal - sized sections (Walk, Run, Stop), so the number of possible outcomes for the spinner is 3.

Step2: Determine outcomes for die

The pyramid - shaped die has 4 sides labeled 1 to 4, so the number of possible outcomes for the die is 4.

Step3: Determine outcomes for coin

A coin has 2 sides (heads and tails), so the number of possible outcomes for the coin is 2.

Step4: Use the multiplication principle

The multiplication principle of counting states that if there are \(n_1\) ways to do the first task, \(n_2\) ways to do the second task, and \(n_3\) ways to do the third task, then the total number of ways to do all three tasks together is \(n_1\times n_2\times n_3\).

Here, \(n_1 = 3\) (spinner), \(n_2=4\) (die), \(n_3 = 2\) (coin).

So the total number of possible outcomes is \(3\times4\times2=24\).

Answer:

24