Question

A game is played were a player spins an arrow pinned to the center of a circle and
wins a prize based on what pie piece the arrow comes to rest on. 40% of the pie wins a
$1 prize, 30% gives a $2 prize, 15% gives a $5 prize, 10% gives a $10 prize, and 5%
gives a $15 dollar prize.

a) What is the expected value of playing this game?

b) If the game costs $4 to play, what percentage of the time do you come out winning
more than you pay?

c) If the game costs $4 to play, and it is expected that 1,000 will the play it at the carnival
one day. How much money does the carnival expect to make off of this game on that
day?

Answer 1

a) The expected value of the game is computed as the sumproduct of the probabilities of each winning price with the corresponding winning prize here. Therefore the expected value here is computed as:

E(X) = 0.4*1 + 0.3*2 + 0.15*5 + 0.1*10 + 0.05*15 = 3.5

Therefore $3.5 is the expected value of playing the game here.

b) Given that it costs $4 to play, the percentage of time we come out winning more than we pay is computed here as:
P(X > 4) = P(X = 5) + P(X = 10) + P(X = 15) = 0.15 + 0.1 + 0.05 = 0.3
Therefore 0.3 is the required probability here.

c) Given that there are 1000 games played from carnival, the expected amount of money that the carnival expected to make is computed here as:

= 1000*(4 - E(X))

= 1000*(4 - 3.5) = $500

Therefore $500 is the required expected money here.