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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.2.20
Chapter 3, Problem 3.2.20

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

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Step 1: Understand the problem. We are tasked with finding the probability of two independent events occurring in sequence: tossing a tail on a coin and rolling a number greater than 2 on a die.
Step 2: Recall the Multiplication Rule for independent events. The probability of two independent events A and B occurring is given by P(A and B) = P(A) × P(B).
Step 3: Determine the probability of the first event (tossing a tail). A fair coin has two sides (head and tail), so the probability of tossing a tail is P(Tail) = 1/2.
Step 4: Determine the probability of the second event (rolling a number greater than 2). A standard die has six faces numbered 1 through 6. The numbers greater than 2 are 3, 4, 5, and 6, which is 4 outcomes out of 6. Therefore, P(Number > 2) = 4/6 = 2/3.
Step 5: Apply the Multiplication Rule. Multiply the probabilities of the two events: P(Tail and Number > 2) = P(Tail) × P(Number > 2). Substitute the values P(Tail) = 1/2 and P(Number > 2) = 2/3 into the formula to find the final probability.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Multiplication Rule of Probability

The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the events are tossing a coin and rolling a die, which do not affect each other. This rule is essential for calculating the combined probability of multiple events.
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Probability of Multiple Independent Events

Independent Events

Independent events are those whose outcomes do not influence one another. For example, the result of tossing a coin does not affect the outcome of rolling a die. Understanding that these events are independent is crucial for applying the Multiplication Rule correctly in probability calculations.
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Calculating Probabilities

Calculating probabilities involves determining the likelihood of specific outcomes. For the coin toss, the probability of getting a tail is 1/2, while for the die, the probability of rolling a number greater than 2 (i.e., 3, 4, 5, or 6) is 4/6. Knowing how to compute these probabilities is vital for solving the problem.
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Related Practice
Textbook Question

Board of Directors The University of Colorado Board of Directors has 23 members. One member serves as board chair and another serves as vice chair. Given the names of the 23

board members, what is the probability of randomly selecting the name of the chair and the name of the vice chair? (Source: University of Colorado)

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Textbook Question

37. Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Use technology to find how many ways one polluted lake and five nonpolluted lakes can be chosen.

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Textbook Question

Using a Frequency Distribution to Find Probabilities In Exercises 49-52, use the frequency distribution at the left, which shows the population of the United States by age group, to find the probability that a U.S. resident chosen at random is in the age range. (Source: U.S. Census Bureau)

52. 65 years old and older

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Textbook Question

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

16. You toss a coin four times. What is the probability of tossing tails exactly half of the time?

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Textbook Question

Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be

interviewed about the work environment.

Find the probability of choosing four third-shift workers.

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Textbook Question

80. Unusual Events Can any of the events in Exercises 75-78 be considered unusual? Explain.

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