Question

2. A fair dice is rolled thrice and the outcome of this experiment is recorded.
a. What is the size of the sample space for this experiment?
b. What is the probability that the sum of first and second outcomes is equal to the third outcome?

Answer 1

a) 6^3 = 216

b) let n be for the third time

n = 1 => P = 0

n = 2 => (1, 1) => P = 1/216

n = 3 => (1, 2) and (2, 1) => P = 2/216

n = 4 => (1,3), (3,1), (2,2) => P = 3/216

n = 5 => (1,4), (4,1), (2,3), (3,2) => P = 4/216

n = 6 => (1,5), (5,1), (2,4), (4,2), (3,3) => P = 5/216

TOTAL P = (1+2+3+4+5)/216 = 15/216