Concept explainers
Rolling a Die An eight-sided die is rolled. Find the
a. Getting a 6
b. Getting a number larger than 5
c. Getting an odd number
a.
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,
Substitute 1 for ‘Number of outcomes inA occurs’ and 8 for ‘Total number of outcomes in the sample space’,
Thus, the probability that the outcome is 6is 0.125.
b.
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,
Substitute 3 for ‘Number of outcomes in B’ and8 for ‘Total number of outcomes in the sample space’,
Thus, the probability of getting a number larger than 5 is0.375.
c.
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,
Substitute 4 for ‘Number of outcomes in C’ and8 for ‘Total number of outcomes in the sample space’,
Thus, the probability ofgetting an odd number is0.50.
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Chapter 4 Solutions
Elementary Statistics: A Step By Step Approach
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