SOLUTION: Suppose you pay $3 to roll a fair die with the understanding you will get back 5$ if you roll a 3 or 5, nothing otherwise. What is your expected value ?

Question 1101418: Suppose you pay $3 to roll a fair die with the understanding you will get back 5$ if you roll a 3 or 5, nothing otherwise. What is your expected value ?
Found 3 solutions by math_helper, Fombitz, greenestamps:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
E = 5(2/6) + (-3)(4/6) = (10/6)-(12/6) = -2/6 = -1/3
E = -1/3 or about -0.33333.
This is an unfavorable game since in the long run you are expected to lose 0.33 on each play.
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Made a mistake in my calculations. It is even more unfavorable than I thought.
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The game costs $3 to play.
If you roll 3 or 5, you win $5, so you gain $2 ("+2").
If you roll 1, 2, 4, or 6, you win nothing, so you lose $3 ("-3").

The expected value is then

On average, you should expect to lose $4 for every 3 games played.
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