## After paying ​$5 to​ play, a single fair die isa single fair die is ​rolled, and you are paid back the number of dollars corresponding to th Question After paying ​$5 to​ play, a single fair die isa single fair die is ​rolled, and you are paid back the number of dollars corresponding to the numberthe number of dots facing up. For​ example, if aa 66 turns​ up, ​$66 is returned to you for a net​ gain, or​ payoff, of​$1, if aa 44 turns​ up, ​$44 is returned for a net gain of minus−​$1, and so on. What is the expected value of the​ game? Is the game​ fair?

in progress 0
1 week 2021-11-25T17:59:49+00:00 1 Answer 0 views 0

No, the game is not fair since the expected value represents a loss.

Step-by-step explanation:

The expected value of this game is calculated using

Where is the net gain of each outcome and is the probability of each outcome.

When a die is rolled, the probability of getting each outcome is

Where 6 is the total number of possible outcomes.

The cost of playing the game is \$5

The net gain for each outcome is given by

Now we can find the expected value of this game,

Since the probability of each outcome is same

Therefore, we can conclude that this game is not fair since the expected value is negative which represents a loss rather than a gain.