Question

If we roll the die 100 times then what is the expected value of the sum for a game where we get ten points if we roll a 5 or a 6 and eight points for any other number.

Answer 1

Solution:

We roll the die 100 times. n = 100

Outcomes of die = 1,2,3,4,5,6

Probability of getting any number = 1/6 = 0.166667

Probability of getting 5 or 6 = (1/6)+(1/6) = 2/6 = 1/3 = 0.333333

Expected number of getting 5 or 6 = 100*0.333333 = 33.33333

(Outcomes are independent)

Probability of getting any other number excluding 5 and 6 = 4/6 = 2/3 = 0.666667

Expected number of getting any other numbers = 100* 0.666667 = 66.6667

Points for getting 5 or 6 = 10

Points for getting any other number = 8

Expected value of the sum = 10*33.33333 + 8*66.6667

Expected value of the sum of points = 866.6669

Required answer = 866.6669