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
9
.
Event
B
: The sum is not divisible by
4
and not divisible by
6
.
Write your answers as exact fractions.

Answer 1

The probability of rolling a sum greater than 9 (Event A) with a fair six-sided die twice is 1/6. The probability of rolling a sum not divisible by 4 and not divisible by 6 (Event B) is 5/12.

Step-by-step explanation:

With a fair six-sided die, the sum of two rolls can range from 2 to 12. We will calculate the probabilities for two specific events using the possible combinations.

Event A: Sum greater than 9

For the sum to be greater than 9, the possible combinations are (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6). Since there are a total of 36 possible outcomes when rolling two dice, the probability for Event A is 6/36 or 1/6.

Event B: Sum not divisible by 4 and not divisible by 6

For the sum to meet Event B's conditions, we need to exclude any sums that are multiples of 4 or 6. The sums that are not divisible by 4 or 6 include: 2, 3, 5, 7, 10, and 11. There are 15 combinations that result in these sums, so the probability for Event B is 15/36 or 5/12.

Answer 2

the cube has 6 side.