Concept explainers
Rolling Two Dice If two dice are rolled one time, find the probability of getting these results:
a. A sum of 5
b. A sum of 9 or 10
c. Doubles
a.
To obtain: The probability of getting an outcome as sum of 5.
Answer to Problem 15E
The probability of getting an outcome as sum of 5 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 event A denote that the outcome as sum of 5. Hence, the possible outcomes to get the sum 5 are ‘
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’,
Thus, the probability that the outcome is sum of 5 is
b.
To obtain: The probability of getting an outcome is sum of 9 or sum 10.
Answer to Problem 15E
The probability of getting an outcome is sum of 9 or sum 10 is
Explanation of Solution
Calculation:
Here, the event B is defined getting sum of 9.
Hence, the possible outcomes are ‘
The probability of event B is,
Substitute 4 for ‘Number of outcomes in B’ and 36 for ‘Total number of outcomes in the sample space’,
Here, the event C is defined as getting a sum of 10. Hence, the possible outcomes for sum 10 are ‘
The probability of event C is,
Substitute 3 for ‘Number of outcomes in C’ and 36 for ‘Total number of outcomes in the sample space’,
The formula for probability of event B and C is,
Substitute 0 for ‘Number of outcomes in B and C’ and 36 for ‘Total number of outcomes in the sample space’,
Addition Rule:
The formula for probability of getting event B or event C is,
Substitute
Thus, the probability of getting an outcome is sum of 9 or sum 10 is
c.
To obtain: The probability of getting doubles.
Answer to Problem 15E
The probability of getting doubles is
Explanation of Solution
Calculation:
Let the event D denote getting doubles.
Hence, the possible outcomes are ‘
The formula for probability of event D is,
Substitute 6 for ‘Number of outcomes in D’ and 36 for ‘Total number of outcomes in the sample space’,
Thus, the probability that the outcome is doubles is
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