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 succes

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 not divisible by
2
and not divisible by
6
.

Answer 1

 

 

Event B:  not divisible by 2 eliminates all evens, giving odds 3-11; not divisible by 6 eliminates 6 and 12 totals only; the net is inclusion of all odds 3-11 when these two sets are intersected.

 

B: even sums are disallowed, period (some but not all of these excluded evens are also divisible by 6).

P(sum=3) = 2/36

P(sum=5) = 4/36

P(sum=7) = 6/36

P(sum=9) = 4/36

P(sum=11) = 2/36

P(sum is not divisible by 2) = 18/36 = ½

 

Try to figure out P(sum>6) by yourself.