If a standard six-sided die is rolled twice, what is the probability that the result of the second roll is not less than the result of the first roll?Express your answer as a common fraction.

Question

If a standard six-sided die is rolled twice, what is the probability that the result of the second roll is not less than the result of the first roll?Express your answer as a common fraction.

Answer 1

x1 = result of first roll, x2 result of second roll. Then by synmetry:

P(x1<x2) = P(x1>x2) (1)

We also know that:

P(x1 = x2) = 1/6 (2)

Since either x1<x2, or x1>x2 or x1 = x2 and all these three possibilites are mutually exclusive we have:

P(x1<x2) + P(x1>x2) + P(x1 = x2) = 1

Using (1) and (2) you then find:

2 P(x1>x2) + 1/6 = 1 ---->

P(x1<x2) = 5/12

And

P(x1<= x2) = P(x1<x2) + P(x1=x2) = 7/12