SOLUTION: Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 4 or a 6, nothing otherwise. What is your expected value?

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Question 1176431: Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 4 or a 6, nothing otherwise. What is your expected value?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.

Of the total 36 possible outcomes, there are 3 (three) outcomes to get the sum of 4,


and there are 5 outcomes to get the sum of 6.


The probability to win is,  THEREFORE,   =  = .


Expected value of the game is   = -1.89 dollars per game.


It means that statistically, you lose 1.89 at each game, in average.

Solved, answered, explained and completed.

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    - Math expectation of winning in games with rolling pair of dice
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Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


The other tutor answered a different problem, using a pair of dice instead of a single die.

Since the die is fair, the probabilities of each number coming up are the same. So the expected value is the average gain or loss if the game is played 6 times and you get each number once.

In doing that, you pay $18 ($3 for each of the 6 rolls) and you get $10 back. You played the game 6 times and lost $8; your average gain/loss is (-18+10)/6 = -4/3.

ANSWER: your expected value is -4/3, meaning on average you will lose about $1.33 each time you play.
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