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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 5
.
Event B
: The sum is an odd number.

Round your answers to at least two decimal places.

Answer 1

event B is easy, as half the outcomes are even, half odd

so P(B) = 1/2 = 50%

P(A) = P(6 through 12) = 25/36 = 69 4/9 = 69.444...%

Answer 2

 

 Consider the following table:

 

         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

 

 

Where the first row is the first dice and the first column in the 2nd dice.

 

For example, the probability of rolling a 7, is 6/36 = 1/6 = 16 and 2/3%. Notice the 7 appears

in the table 6 times, out of the 36 possible outcomes.

 

Event A:

  Prob( 6 or 7 or 8 or 9 or 10 or 11 or 12) = 5/36 + 6/26 + 5/36 + 4/36 + 3/36 + 2/36 = 25/36 = .694444.... 

                                                                                                                                    69.44444.....%

 

    It is reduced to lowest terms because 25  = 5x5 and 5 does not divide 36. 

 

Event B:

  prob( 3 or 5 or 7 or 9 or 11) = 2/36 + 4/36 + 6/36 + 4/36 + 2/36b=  18/36 = 1/2 = 0.5 = 50%