Concept explainers
Suppose that two balanced dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. What is the
- a a sum of 3 before we obtain a sum of 7?
- b a sum of 4 before we obtain a sum of 7?
a.
Find the probability that a sum of 3 before people obtain a sum of 7.
Answer to Problem 119E
The probability that a sum of 3 before people obtain a sum of 7 is 0.25.
Explanation of Solution
Calculation:
Let A denotes a sum is 3 and B denotes a sums are not 3 or not 7
The possible outcomes when two dice are tossed.
Total number of outcomes is 36.
The list of outcomes for getting a sum of 3 is {(1,2), (2,1)}. Therefore, the number of ways of getting a sum of 3 is 2.
The list of outcomes for getting a sum of 7 is {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}. Therefore, the number of ways of getting a sum of 7 is 6.
The probability of getting an event A is
The probability of getting an event B is
Here, a sum of 3 before sum of 7 can happen on the first roll, second roll, third roll, etc. This can be written as, A, BA, BBA, BBBA, etc
The probability that a sum of 3 before people obtain a sum of 7 is obtained as follows:
Thus, the probability that a sum of 3 before people obtain a sum of 7 is 0.25.
b.
Find the probability that a sum of 4 before people obtain a sum of 7.
Answer to Problem 119E
The probability that a sum of 4 before people obtain a sum of 7 is 0.3333.
Explanation of Solution
Calculation:
Let A denotes a sum is 4 and B denotes a sums are not 4 or not 7
The list of outcomes for getting a sum of 4 is {(1,3),(2,2) (3,1)}. Therefore, the number of ways of getting a sum of 3 is 3.
The list of outcomes for getting a sum of 7 is {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}. Therefore, the number of ways of getting a sum of 7 is 6.
The probability of getting an event A is
The probability of getting an event B is
Here, a sum of 4 before sum of 7 can happen on the first roll, second roll, third roll, etc. This can be written as, A, BA, BBA, BBBA, etc
The probability that a sum of 4 before people obtain a sum of 7 is obtained as follows:
Thus, the probability that a sum of 3 before people obtain a sum of 7 is 0.3333.
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Chapter 2 Solutions
MATH.STATISTICS W/APPL.-ACCESS
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning