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?

Step-by-step 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

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

Thus, the expected point he can earn in one throw

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt