Question

After paying ​$5 to​ play, a single fair die is ​rolled, and you are paid back the number of dollars corresponding to the number of dots facing up. For​ example, if a 6 turns​ up, ​$6 is returned to you for a net​ gain, or​ payoff, of​ $1, if a 4 turns​ up, ​$4 is returned for a net gain of minus​$1, and so on. What is the expected value of the​ game? Is the game​ fair? The expected payoff of the game is ​$ nothing.

Answer 1

Answer:

-$1.5

Unfair game as you are expected to lose money

Step-by-step explanation:

There's 1/6 chance of getting 1 face of the dice.

So the expected gain from the game is

$6*\frac{1}{6} + 5*\frac{1}{6} + 4*\frac{1}{6} + 3*\frac{1}{6} + 2*\frac{1}{6} + 1*\frac{1}{6} = \frac{1}{6}*(1+2+3+4+5+6) = \frac{21}{6} = 3.5$

Since the cost to play game is $5, the expected value of the game is

$3.5 - $5 = -$1.5

Since this is a negative amount, the game is unfair. You are losing $1.5 as you play.