Question

An ordinary (fair) die is a cube with the numbers through 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 . Event : The sum is not divisible by .

Answer 1

Complete question :

Compute the probability of each of the following events.

Event : The sum is greater than 6

Event : The sum is not divisible by 2

Answer:

7/12 ; 1/2

Explanation:

Sample space :

2, 3, 4, 5, 6, 7

3, 4, 5, 6, 7, 8

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9, 10

6, 7, 8, 9, 10, 11

7, 8, 9, 10, 11, 12

Probability that sum is greater than 6:

Number of outcomes greater Than 6 = required outcomes = (7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12) = 21

Total sample space = total possible outcomes = 36

Probability = required outcome / Total possible outcomes

P(sum is greater Than 6) = 21 / 36

2.)

Obtaining an even number :

Sum not divisible by 2 = required outcomes = (3, 5, 7, 3, 5, 7, 5, 7, 9, 5, 7, 9, 7, 9, 11, 7, 9, 11) = 18

Total sample space = total possible outcomes = 36

P(sum is not divisible by 2) = 18 / 36 = 1 / 2