die rolling events and probability

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: The sum is greater than 9.
Event: The sum is not divisible by 3 and not divisible by 6.
Round your answers to at least two decimal places.

Answer 1

Make an array of the six-by six possibilities: 

# of ways to get a sum = two is just 1 (1,1)

# of ways to get a sum = three is two (1,3) & (2,1)

# ways to get a sum = four is three

# ways to get a sum = five is four, ETC.

 

    1  2  3  4  5  6  

1| 2  3  4  5  6  7

2| 3  4  5  6  7  8

3||4  5  6  7  8  9

4| 5  6  7  8  9  10

5| 6  7  8  9  10 11

6| 7  8  9  10 11 12

 

p(Sum>9) = p(10) +p(11) + P (12) = 3/36 + 2/36 + 1/36 = 6/36 = 1/6.

 

Use the above table to answer any questions based on two dice totals probabilities.