What is the probability of the total being greater than 8 out of rolling two dice?

Answer 1

.277

Explanation:

The regular 6 face dye has 6 possible outcomes. Two dice have 6 x 6 = 36 possible

outcomes (single events). Let x be the discrete random variable equal to the sum

of the outcome of each of the two dice tossed. Then the sample space is,

x = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

For x = 2: one event; (1,1). Probability of x = 2, P(x=2) = 1/36

for x = 3: two events; (1,2), (2,1). P(x=3) = 2/36 = 1/18

for x = 4: three events; (1,3), (3,1), (2,2). P(x=4) = 3/36 = 1/12

for x = 5: four events; (1,4), (4,1), (2,3), (3,2). P(x=5) = 4/36 = 1/9

for x = 6: five events; (1,5),(5,1), (2,4), (4,2), (3,3). P(x=6) = 5/36

for x = 7: six events; (1,6), (6,1), (2,5), (5,2), (3,4), (4,3). P(x=7) = 6/36 = 1/6

for x = 8: five events; (2,6), (6,2), (3,5), (5,3), (4,4). P(x=8) = 5/36

for x = 9: four events; (3,6), (6,3), (4,5), (5,4). P(x=9) = 4/36 =1/9

for x = 10: three events; (4,6), (6,4), (5,5). P(x=10) = 3/36 = 1/12

for x = 11: two events; (5,6), (6,5). P(x=11) = 2/36 = 1/18

For x = 12: one event; (6,6). P(x=12) = 1/36

Question: P(x>8) = P(x=9)+P(x=10)+P(x=11)+P(x=12) =

4/36 + 3/36 + 2/36 + 1/36 = 10/36 = 5/18 = 0.277... ≈ 27.8%