Three dice are tossed. The red die has 8 sides (labeled 1 to 8), the blue die ha

Question

Three dice are tossed. The red die has 8 sides (labeled 1 to 8), the blue die has 8 sides (labeled 0 to 7) and the grey die has 3 sides (labeled -3 to -1). The red die has a "3x multiplier" status, and the grey die has a "2x multiplier" and counts for negative points. The total of the dice is how many points you win.
Assuming you want points, what is the best possible number of points you can win?  
What is the chance of that happening?  

What is the worst possible number of points you can win?  
What is the chance of that happening?  

What is the average number of points for each roll?

Explanation / Answer

Points you win = 3xoutcome of die 1 + 2xoutcome of die 2 + outcome of die 3

Best possible number of points you can win = 3x8 + 2x7 -1

= 37

P(best possible points) = 1/8 x 1/8 x 1/3

= 0.0052

Worst possible point you can win = 3x1 + 2x0 -3

= 0

P(worst possible points) = 1/8 x 1/8 x 1/3

= 0.0052

Average number of points = 3x(1+8)/2 + 2x(0+7)/2 + (-1-3)/2

= 13.5 + 7 - 2

= 18.5

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