Ivanna is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random.

This game is this: Ivanna spins the spinner once. She wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner stops on the number 3, and $7 if the spinner stops on the number 4. She loses $8 if the spinner stops on 5 or 6.

The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.

I guess that we want to find the expected value in one spin:

number 1: wins $1

number 2: wins $3

number 3: wins $5

number 4: wins $7

number 5: losses $8

number 6: loses $8

The expected value can be calculated as:

Ev = ∑xₙpₙ

where xₙ is the event and pₙ is the probability.

We know that the probability for all the events is 1/6, so we have:

Ev = ($1 + $3 + $5 + $7 - $8 - $8) * (1/6) = $0

So the expected value of this game is $0, wich implies that is a fair game.