Event A : The sum is greater than 6 . Event B : The sum is divisible by 6 .

Question

An ordinary (fair) die is a cube with the numbers
1
through
6
on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events:
Event
A
: The sum is greater than
6
.
Event
B
: The sum is divisible by
6
.
Write your answers as exact fractions.

Answer 1

If you roll 2 six-sided die (D6) there are a variety of outcomes that are possible.

As each roll is independent of each other and there are 6 possible results for each D6, rolling two dice gives you 6 * 6 = 36 possible results.

 

For Event A:

If the first dice rolled is 1, then there is 1 possible result the second D6 can roll, if added with the first number yields a sum greater than 6 (6). If the first dice is a 2, then there are two possible results the second dice can have (6, 5) to yield a sum greater then 6, and so on.

Adding these possible combinations together is 1+2+3+4+5+6 = 21, 21 possible combinations / 36 total combos = 7/12 = 0.58

 

For Event B:

There are only two possible sums which are divisible by 6, 6 and 12. However, there are multiple combinations that can have a sum of 6: 1&5, 2&4, 3&3, 4&2, 5&1, and one combo that can yield 12: 6&6;

6 possible combinations / 36 total combos = 1/6 = 0.17