SOLUTION: In a simple game, a six-sided die is rolled 4 times. If all four rolls result in either 1 or 2, then the player wins $50 dollars. If the player has to pay $10 to play the game, w

Question 1012911: In a simple game, a six-sided die is rolled 4 times. If all four rolls result in either 1 or 2, then the player wins $50 dollars. If the player has to pay $10 to play the game, what are the expected winnings of the player over time if many games are played?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you roll a fair die once, the probability of getting a 1 or a 2 is 1/3. The probability of 4 successes in 4 trials where the probability of success on one trial is:

So over the long run you win 1 time every 81 times you play, and you lose 80 times every 81 times you play. When you win, you pay $10 and get $50 back for a net gain of $40. When you lose, you pay $10 and get nothing back for a net gain of -$10.

Hence your per game net is:

And if you played 810 games, you should expect to lose about $7600 overall.

John

My calculator said it, I believe it, that settles it

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