Chapter 4, Problem 4.1.1RE

Rolling a Die An eight-sided die is rolled. Find the probability of each.

a. Getting a 6

b. Getting a number larger than 5

c. Getting an odd number

To determine

To obtain: The probability of getting an outcome as6.

Answer to Problem 4.1.1RE

The probability that the outcome as 6is 0.

Explanation of Solution

Given info:

A 8-sided die is rolled.

Calculation:

Onrolling an 8-sided die has 8 different outcomes. That is, the outcomes are ‘1, 2, 3, 4, 5, 6, 7 and 8’.

Here, event A denotes an outcome is 6. Hence, the possible outcome is 1 which is 6.

Let event A denote that the outcome is 6.

The formula for probability of event A is,

$P\left(A\right)=\frac{\text{Number of outcomes in }A}{\text{Total number of outcomes in the sample space}}$

Substitute 1 for ‘Number of outcomes inA occurs’ and 8 for ‘Total number of outcomes in the sample space’,

$\begin{array}{c}P\left(A\right)=\frac{1}{8}\\ =0.125\end{array}$

Thus, the probability that the outcome is 6is 0.125.

To determine

To obtain: The probability ofgetting a number larger than 5.

Answer to Problem 4.1.1RE

The probability ofgetting a number larger than 5 is0.375.

Explanation of Solution

Calculation:

Here eventB is defined as rolling a numberlarger than 5. Hence, the possible outcomes that the number larger than 5 are ‘6, 7 and 8’. That is, there are 3 outcomes for eventB.

The probability of event B is,

$P\left(B\right)=\frac{\text{Number of outcomes in }B}{\text{Total number of outcomes in the sample space}}$

Substitute 3 for ‘Number of outcomes in B’ and8 for ‘Total number of outcomes in the sample space’,

$\begin{array}{c}P\left(B\right)=\frac{3}{8}\\ =0.375\end{array}$

Thus, the probability of getting a number larger than 5 is0.375.

To determine

To obtain: The probability ofgetting an odd number.

Answer to Problem 4.1.1RE

The probability ofgetting an odd number is0.50.

Explanation of Solution

Calculation:

Here, the eventC is defined as rolling an odd number. Hence, the possible outcomes for odd numbers are ‘1, 3, 5 and 7’. That is, there are 4 outcomes for eventC.

The probability of event C is,

$P\left(C\right)=\frac{\text{Number of outcomes in }C}{\text{Total number of outcomes in the sample space}}$

Substitute 4 for ‘Number of outcomes in C’ and8 for ‘Total number of outcomes in the sample space’,

$\begin{array}{c}P\left(C\right)=\frac{4}{8}\\ =0.50\end{array}$

Thus, the probability ofgetting an odd number is0.50.