Concept explainers
Rolling Two Dice When two dice are rolled, find the
a. A sum greater than 9
b. A sum less than 4 or greater than 9
c. A sum that is divisible by 4
d. A sum of 14
e. A sum less than 13
a.

The probability of getting a sum of 5 or 6.
Answer to Problem 4.1.6RE
The probability of gettinga sum of 5 or 6 is
Explanation of Solution
Given info:
Two dices are rolled.
Calculation:
When two dices are rolled the sample space is
Thus, the total number of outcomes is 36.
Let event A denote getting a sum 5.
Hence, the possible outcomes for getting a sum 5 are,
That is, there are 5 outcomes for event A.
The formula for probability of event A is,
Substitute 4 for ‘Number of outcomes in A’ and 36 for ‘Total number of outcomes in the sample space’,
Let event B denote getting a sum 6.
Hence, the possible outcomes for getting a sum 6 are,
That is, there are 5 outcomes for eventB.
The formula for probability of event B is,
Substitute 5 for ‘Number of outcomes in B’ and 36 for ‘Total number of outcomes in the sample space’,
Addition Rule:
The formula for probability of getting event A or event B is,
Substitute
Thus, the probability that the outcome is sum of 5 or 6 is
b.

To obtain: The probability of getting a sum greater than 9.
Answer to Problem 4.1.6RE
The probability of getting a sum greater than 9 is
Explanation of Solution
Calculation:
Let event C denote getting a sum greater than 9.
Hence, the possible outcomes for getting a sum greater than 8 are,
That is, there are 6 outcomes for eventC.
The formula for probability of event C is,
Substitute 6 for ‘Number of outcomes in C’ and 36 for ‘Total number of outcomes in the sample space’,
Thus, the probability of getting a sum greater than 9is
c.

To obtain: The probability of getting a sum less than 4 or greater than 9.
Answer to Problem 4.1.6RE
The probability of getting a sum less than 4 or greater than 9 is
Explanation of Solution
Calculation:
Let event D denote getting a less than 4.
Hence, the possible outcomes for getting a sum less than 4are,
That is, there are 3 outcomes for eventD.
The formula for probability of event D is,
Substitute 3 for ‘Number of outcomes in D’ and 36 for ‘Total number of outcomes in the sample space’,
Let event E denote getting a sum greater than 9.
Hence, the possible outcomes for getting a sum greater than 9are,
That is, there are 6 outcomes for eventE.
The formula for probability of event E is,
Substitute 6 for ‘Number of outcomes in E’ and 36 for ‘Total number of outcomes in the sample space’,
Addition Rule:
The formula for probability of getting event A or event B is,
Substitute
Thus, the probability of getting a sum less than 4 or greater than 9is
d.

To obtain: The probability of getting a sum divisible 4.
Answer to Problem 4.1.6RE
The probability of getting a sum divisible 4is
Explanation of Solution
Calculation:
Let event E denote getting a sum divisible by4.
Hence, the possible outcomes for getting a sum divisible 4are,
That is, there are 12 outcomes for eventE.
The formula for probability of event E is,
Substitute 9 for ‘Number of outcomes in E’ and 36 for ‘Total number of outcomes in the sample space’,
Thus, the probability of getting a sum divisible 4is.
e.

To obtain: The probability of getting a sum of 14.
Answer to Problem 4.1.6RE
The probability of getting a sum of 14is0.
Explanation of Solution
Calculation:
Let event F denote getting a sum of 14.
Here, the number of possible outcomes for getting a sum of 14 is 0.
That is, there are 0 outcomes for eventF.
The formula for probability of event F is,
Substitute 0 for ‘Number of outcomes in F’ and 36 for ‘Total number of outcomes in the sample space’,
Thus, the probability of getting a sum of 14is0.
f.

To obtain: The probability of getting a sum less than 13.
Answer to Problem 4.1.6RE
The probability of getting a sum less than 13is1.
Explanation of Solution
Calculation:
Let event G denote getting a sum less than 13.
Hence, the possible outcomes for getting a sum less than 13are,
That is, there are 36 outcomes for eventG.
The formula for probability of event G is,
Substitute 36 for ‘Number of outcomes in F’ and 36 for ‘Total number of outcomes in the sample space’,
Thus, the probability of getting a sum less than 13is1.
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Chapter 4 Solutions
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