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A and B play a game by rolling 2 dice. A gets 5 points if he rolls a double (both dice the same), otherwise he loses 1 point. Is the game fair? What is the expectation gain or loss for A? Is probability distribution table necessary?

I tried calculate $E(x)$.

$5(6/12)+(-1)(15/21)=5/7$

but $E(x) = 0$. Did I miss something?

George V. Williams
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frizz
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    What have you tried? Where are you stuck? You should not need any distribution table. It might help to think of all possible combination of dice. – snoram Jul 17 '16 at 14:48
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  • I tried calculate the expectation values – frizz Jul 17 '16 at 14:50
  • 5(6/12)+(-1)(15/21)=5/7 but e(x) =0 Did I miss something? – frizz Jul 17 '16 at 14:52
  • There are 36 possible combinations. And much less than half of them are "a double". – snoram Jul 17 '16 at 14:56
  • Can you explain why it is 36 possible combinations? I really need help on this. Thank you. – frizz Jul 17 '16 at 15:00

1 Answers1

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As can be seen from the picture below there are 36 possible combination of two die. All are equally likely (assuming the die are not rigged), thus the probability of both die showing the same number is $\frac{6}{36}$ and the probability that they don't is $1-\frac{6}{36} = \frac{30}{36}$.

$\hskip2in$ Picture source: https://casmusings.wordpress.com/

snoram
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  • Oh I see my problem there. I did not count the opposite site . OK thanks for your explanation. Have a nice day :) – frizz Jul 17 '16 at 15:19