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 8 .Event B : The sum is an odd number.Write your answers as fractions.

Answer 1

Given: A die rolled twice in succession and the face values of the two rolls are added together

To Determine: The probability that

(a) the sum is greater than 8

(b) the sum is an odd number

Solution

The sample space of the events is as shown below

Determine the elements of events A

$\begin{gathered} A=\lbrace x|x>8\rbrace \\ A=\lbrace9,10,11,12\rbrace \\ B=\lbrace x|x\text{ is odd\rparen\textbraceright} \\ B=\lbrace3,5,7,9,11\rbrace \end{gathered}$

From the sample space, it can be found that

$\begin{gathered} n(S)=36 \\ n(A)=10 \\ n(B)=18 \end{gathered}$

Where n(S) is the total number in the sample space

n(A) is the total number in the sample space that is greater than 8

n(B) is the total number in the sample space that is odd

Note that the probability of an event A is is given as

$P(A)=\frac{n(A)}{n(S)}$

Therefore

$\begin{gathered} P(A)=\frac{10}{36}=\frac{5}{18} \\ P(B)=\frac{18}{36}=\frac{1}{2} \end{gathered}$

Hence, the probability of getting a sum greater than 8 is 5/18

The probability of getting an odd sum is 1/2