Question

A player rolls two dice, if the player rolls a sum of 7, the player earns $15. if the player rolls a sum greater than 7, the player pays $6. if the player rolls a sum less than 7, the player pays nothing.

what is the amount winning probability?

Answer 1

If we see the probability of each pair of numbers appearing on rolling the die, we get above chart. Each pair has a probability of (1/6)*(1/6)=1/36

Green color => player rolls a sum less than 7 ( if you add the numbers on pair of die it's < 7)

Yellow color => player rolls a sum of 7

Orange color => player rolls a sum greater than 7

Thus p(<7)= 15/36, p(=7)=6/36 AND p(>7)=15/36

Therefore, Expected value = -6*P(p>7)+15*p(=7)+0*p(<7)= -6*(15/36)+15*(6/36)=0