Question

Harlene tosses two number cubes. If a sum of 8 or 12 comes up, she gets 9 points. If not, she loses 2 points. What is the expected value of the number of points for one roll?

Answer 1

Answer:
`-(1)/(6)`

Explanation:

Since, the total outcomes when two dices are thrown = 36

Also, the total outcomes of getting the sum of 8 or 12 in throwing = {(2,6)(6,2)(3,5),(5,3),(4,4)}= 6

Hence, the probability of getting the sum of 8 or 12 in throwing two dices

`= (6)/(36)=(1)/(6)`

Also, the probability of getting the sum of 8 or 12 in throwing two dices
`= 1-(1)/(6)=(5)/(6)`

Thus, the expected point he can earn in one throw
`= 9* (1)/(6)-2* {5}{6} = (9)/(6)-(10)/(6)=-(1)/(6)`

Answer 2

It's easy enough. Solving looks like that: p(roll of 8)+p(roll of 12) =
`(5)/(36) + (1)/(36) = (1)/(6) ; (1)/(6) *9 +(5)/(6)*2 = (3)/(2) - (5)/(3) = -(1)/(6)` Hope everything is clear.