Question

avani 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 spins a spinner with four equal - sized sections labeled red, green, blue, orange and flips a coin?

Explanation:

Step1: Determine outcomes for spinner

The spinner has 4 equal - sized sections, so the number of possible outcomes for the spinner, let's call it \(n_{spinner}\), is 4.

Step2: Determine outcomes for coin flip

A coin has 2 sides (Heads and Tails), so the number of possible outcomes for the coin flip, let's call it \(n_{coin}\), is 2.

Step3: Use the multiplication principle

The multiplication principle of counting states that if there are \(m\) ways to do one thing and \(n\) ways to do another thing, then there are \(m\times n\) ways to do both things. Here, to find the total number of possible outcomes for spinning the spinner and flipping the coin, we multiply the number of outcomes of the spinner and the number of outcomes of the coin. So the total number of outcomes \(N=n_{spinner}\times n_{coin}\).
Substituting the values, we get \(N = 4\times2=8\).

Answer:

8