A person spins the pointer and is awarded the amount indicated by the pointer.

(A circle with 3 sections divided: $2, $5, $10). The pointer stops on $2.

It costs $6 to play the game. Determine:


a.) The expectation of a person who plays the game.

b.) The fair price to play the game.

expected value

= (1/3)($2) + (1/3)($5) + (1/3)($10) = $5.67

Draw your conclusion.

what do you mean by draw your conclusion?

To determine the expectation and fair price of playing the game, we first need to understand the concept of expected value.

The expected value (or expectation) of an event is the average value we can expect to get if we repeat the event many times. It is calculated by multiplying each outcome by its probability, and then summing up the products.

a.) To determine the expectation of a person who plays the game, we need to consider the payouts and their probabilities. In this game, there are three possible outcomes: $2, $5, and $10. The probabilities for each outcome depend on the fairness of the game, and assuming each section on the wheel is equally likely to be landed on, we can assign the probabilities as 1/3 for each outcome.

To calculate the expectation, we multiply each outcome by its probability and sum them up:

(Probability of $2) * (Payout of $2) + (Probability of $5) * (Payout of $5) + (Probability of $10) * (Payout of $10)

(1/3) * $2 + (1/3) * $5 + (1/3) * $10 = $2/3 + $5/3 + $10/3 = $17/3 ≈ $5.67

Therefore, the expectation for a person who plays the game is approximately $5.67.

b.) The fair price of playing the game is the amount that would make the game have an expected value of 0. In other words, it is the price at which a person's expected gain or loss from playing the game is zero.

Since the game costs $6 to play, we need to find the amount that, when subtracted from the expectation, equals zero.

$5.67 - (Amount spent on the game) = 0

Solving for the amount spent on the game:

$5.67 - (Amount spent on the game) = 0
Amount spent on the game = $5.67

Therefore, the fair price to play the game is approximately $5.67.