Thursday, 14 November 2013

Probability and expected value of rolling two dice with a twist

Let this be a game with two phases.



In phase 1, roll two 6-sided dice and compute the difference between the rolls. Call this difference x.
In phase 2, roll x dice, and add up the total of the rolls. This is the payout in dollars of the game.



In the first phase of the game, x can take on any value 0 to 5. Compute the probability (as a fraction)
Now for the second phase of the game, for each value of x, what is the average payout (expected value) of the game?




Now I believe I got the right probabilities for 0 - 5, but I'm questioning if i'm doing the second part correctly.



When x=0 I said E(X)=0



And for x=1 I said that E(X)=10363.5



Is this correct? My reasoning was the expected value for rolling a 6 sided die, would be 3.5 and since we have a 1036 of getting a value of 1 in the first part we need to multiply 3.5 by it.



Is this the correct logic? Thanks!!

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