Concept explainers
Rolling Two Dice If two dice are rolled one time, find the probability of getting these results:
a. A sum less than 9
b. A sum greater than or equal to 10
c. A 3 on one die or on both dice.
a.
To obtain: The probability of getting a sum less than 9.
Answer to Problem 16E
The probability of getting a sum less than 9 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 getting a sum less than 9.
Hence, the possible outcomes some less than 9 are,
That is, there are 26 outcomes for event A.
The formula for probability of event A is,
Substitute 26 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 less than 9 is
b.
To obtain: The probability of getting a number greater than or equal to 10.
Answer to Problem 16E
The probability of getting a number greater than or equal to 10 is
Explanation of Solution
Calculation:
Here, the event B is defined as rolling a number greater than or equal to 10. Hence, the possible outcomes greater than or equal to 10 are ‘
The probability of event B is,
Substitute 6 for ‘Number of outcomes in B’ and 36 for ‘Total number of outcomes in the sample space’,
Thus, the probability of getting a number greater than or equal to 10 is
c.
To obtain: The probability of getting an outcome 3 on one die or 3 on both dice.
Answer to Problem 16E
The probability of getting an outcome 3 on one die or 3 on both dice is
Explanation of Solution
Calculation:
Here event C is defined as rolling a number 3 on one die.
Hence, the possible outcomes for 3 on one die are
That is, there are 10 outcomes for event B.
The probability of event C is,
Substitute 10 for ‘Number of outcomes in C’ and 36 for ‘Total number of outcomes in the sample space’,
Here, the event D is defined as rolling a number 3 on both dice.
Hence, the possible outcome for 3 on both dice is
Substitute 1 for ‘Number of outcomes in D’ and 36 for ‘Total number of outcomes in the sample space’,
The formula for probability of event C and D is,
Substitute 0 for ‘Number of outcomes in C and D’ and 36 for ‘Total number of outcomes in the sample space’,
Addition Rule:
The formula for probability of getting event C or event D is,
Substitute
Thus, the probability of getting an outcome 3 on one die or 3 on both dice is
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Chapter 4 Solutions
Elementary Statistics: A Step-by-Step Approach with Formula Card
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