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5 votes
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?

2 Answers

3 votes

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)

User Mdew
by
7.8k points
3 votes
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.
User Misterhex
by
7.8k points
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