Question

If a standard six-sided die is rolled twice, what is the probability that the second number rolled is not less than the first number

rolled? Express your answer as a common fraction.

Answer 1

`(7)/(12)`

Explanation:

Probabilities

When rolling a dice twice, we can get 36 different combinations of the numbers, starting from (1,1),(1,2),(1,3),... up to (6,4),(6,5),(6,6).

From those combinations, only those where the second number rolled is not less than the first number are favorable outcomes.

Thus, the favorable outcomes are:

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,2),(2,3),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6),

(4,4),(4,5),(4,6),(5,5),(5,6),(6,6)}

The total number of favorable outcomes is: 21. Thus the required probability is:

p=\frac{21}{36}=\frac{7}{12}

Answer:
`(7)/(12)`