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.Write your answers as fractions.(a) PA = (b) PB =
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.Write your answers as fractions.(a) PA = (b) PB =
Solution 1
To solve this problem, we first need to understand the total number of possible outcomes when rolling a die twice. Since a die has 6 faces, the total number of outcomes is 6*6 = 36.
(a) Event A: The sum is greater than 5.
The possible outcomes where the sum is greater than 5 are: (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). That's 24 outcomes. So, the probability PA = 24/36 = 2/3.
(b) Event B: The sum is an odd number.
The possible outcomes where the sum is an odd number are: (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5). That's 18 outcomes. So, the probability PB = 18/36 = 1/2.
Solution 2
To solve this problem, we first need to understand the total number of possible outcomes when rolling a die twice. Since a die has 6 faces, the total number of outcomes is 6*6 = 36.
(a) Event A: The sum is greater than 5.
The possible outcomes where the sum is greater than 5 are: (2,4), (2,5), (2,6), (3,3
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