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.
a) expected value: 2*1/3 + 5*1/3 + 10*1/3
1/3(2+5+10)=17/3 dollars
fair price: 5.67
To determine the expectation of a person who plays the game, we need to calculate the average amount they can expect to win or lose.
a.) The expectation is calculated by multiplying the amount won or lost for each outcome by the probability of that outcome occurring, and then summing up these values. In this case, there are three possible outcomes: winning $2, winning $5, or winning $10. The probabilities of each outcome can be calculated by considering the number of sections corresponding to each amount and dividing it by the total number of sections on the circle.
The pointer stops on $2, which means the person wins $2. The probability of this outcome is 1/3, because there is one section out of three that represents winning $2.
To calculate the expectation, we multiply the amount won by the corresponding probability for each outcome, and sum up these values:
Expectation = (Amount won for each outcome) x (Probability of each outcome)
Expectation = ($2) x (1/3) + ($5) x (0) + ($10) x (0)
Expectation = $2/3
Therefore, the expectation of a person who plays the game is $2/3.
b.) To determine the fair price to play the game, we need to consider the expectation. The fair price is the maximum amount a person should be willing to pay to play the game such that they still have an expected value of $0.
In this case, the expectation is $2/3. To determine the fair price, we set this expectation equal to $0 and solve for the amount paid to play the game:
$2/3 - $6 = 0
$2/3 = $6
1/3 = $6
1 = $6 x 3
$6 = $18
Therefore, the fair price to play the game is $18.