Concept explainers
a.
To obtain: The
a.
Answer to Problem 26CQ
The probability of getting a sum 6 or 7 is
Explanation of Solution
Given info:
A pair of six-sided dice is rolled.
Calculation:
The possibilities for rolling a pair of six-sided dice is,
Thus, the total number of outcomes is 36.
Let
Hence, the possible outcomes for getting a sum 6 are,
That is, there are 5 outcomes for event A.
The formula for probability of event A is,
Substitute 5 for ‘Number of outcomes in A’ and 36 for ‘Total number of outcomes in the
Let event B denote getting a sum 7.
Hence, the possible outcomes for getting a sum 7 are,
That is, there are 6 outcomes for eventB.
The formula for probability of event B is,
Substitute 6 for ‘Number of outcomes in B’ and 36 for ‘Total number of outcomes in the sample space’,
The formula for probability of getting event A or event B is,
Substitute
Thus, the probability that the outcome is sum less than 9 is
b.
To obtain: The probability of getting a sum greater than 8.
b.
Answer to Problem 26CQ
The probability of getting a sum greater than 8 is
Explanation of Solution
Calculation:
Let event C denote getting a sum greater than 8.
Hence, the possible outcomes for getting a sum greater than 8 are,
That is, there are 10 outcomes for eventC.
The formula for probability of event C is,
Substitute 10 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 8 is
c.
To obtain: The probability of getting a sum less than 3 or greater than 8.
c.
Answer to Problem 26CQ
The probability of getting a sum less than 3 or greater than 8 is
Explanation of Solution
Calculation:
Let event D denote getting a less than 3.
Hence, the possible outcomes for getting a sum less than 3 are,
That is, there are 1 outcome for eventD.
The formula for probability of event D is,
Substitute 1 for ‘Number of outcomes in A’ and 36 for ‘Total number of outcomes in the sample space’,
Let event E denote getting a sum greater than 8.
Hence, the possible outcomes for getting a sum greater than 8 are,
That is, there are 10 outcomes for eventE.
The formula for probability of event E is,
Substitute 10 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 3 or greater than 8 is
d.
To obtain: The probability of getting a sum divisible 3.
d.
Answer to Problem 26CQ
The probability of getting a sum divisible 3 is
Explanation of Solution
Calculation:
Let event E denote getting a sum greater than 8.
Hence, the possible outcomes for getting a sum divisible 3 are,
That is, there are 12 outcomes for eventE.
The formula for probability of event E is,
Substitute 12 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 3 is
e.
To obtain: The probability of getting a sum of 16.
e.
Answer to Problem 26CQ
The probability of getting a sum of 16 is0.
Explanation of Solution
Calculation:
Let event F denote getting a sum of 16.
Here, the number of possible outcomes for getting a sum of 16 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 16 is0.
f.
To obtain: The probability of getting a sum less than 11.
f.
Answer to Problem 26CQ
The probability of getting a sum less than 11 is
Explanation of Solution
Calculation:
Let event G denote getting a sum less than 11.
Hence, the possible outcomes for getting a sum divisible 3 are,
That is, there are 33 outcomes for eventG.
The formula for probability of event G is,
Substitute 33 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 11 is
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