Question

. A player rolls a fair die and receives 2 dollars if they roll a 2 and nothing if they don’t roll a two.

1. If the game costs $1.25 to play, how much should the player expect to win or loss over the long run? (4 points)
2. Is this a fair game? Give a reason for your answer, (4 points)

Answer 1

Probability = Favorable Outcomes / Total Outcomes

A dice has 6 faces, Therefore total Outcomes = 6

Probability of getting a 2 = P(2) = 1/6

Net winnings = 2 - 1.25 = 0.75

Probability of Not getting a 2 = P(Not 2) = 5/6

Net winnings = 0 - 1.25 = - 1.25

	x	p(x)
2	1/6	0.75
not 2	5/6	-1.25

(a) Expected Value = SUM[x * P(x)] = [(1/6) * 0.75] + [(5/6) * -1.25] = 0.75/6 - 6.25/6 = -5.75/6 = $-0.9583 $ - 0.96

(b) No this is not a fair game. If it was a fair game then the net expected value should be equal to 0.