Question

You need $5 to play a game of dice. If you roll adouble, you receive $20.If you roll a sum of 10, you get $10. Otherwise, youlose your $5.Will you play this game based on the expected value.Show your work.

Answer 1

We start by looking at the total possible outcome for a game of dice.

We get a total of 36 outcomes.

i.e (1,1), (1,2), (1,3)....(1,6), (2,1),(2,2),...(6,6).

There is only a single chance of rolling a double at a single throw. This interpretes as 1/36

The possible combination of includes (4,6),(5,5) and (6,6). This interpretes as 3/36 or 1/12. Which is one of twelve rolls.

From the above we can conclude that to get either of the two winning option,

`\begin{gathered} Pr(\text{double or sum of 10)} \\ =(1)/(36)+(3)/(36) \\ =(4)/(36) \\ =(1)/(9) \end{gathered}`

Hence, you have 1 in nine chances to win double your money ($10) or $20. This means you have to play a minimum of 9 times to win one of those. This would have cost you $45.

Final answer

So, I will not play this game because the chances of winning is slim