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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.RE.6
Chapter 3, Problem 3.RE.6

In Exercises 5 and 6, use the Fundamental Counting Principle.
6. The state of Virginia's license plates have three letters and four digits. Assuming that any letter or digit can be used, how many different license plates are possible?

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Step 1: Understand the structure of the license plate. The license plate consists of three letters followed by four digits. Each letter can be any of the 26 letters in the English alphabet, and each digit can be any of the 10 digits (0 through 9).
Step 2: Use the Fundamental Counting Principle, which states that if one event can occur in 'm' ways and a second event can occur in 'n' ways, then the total number of ways both events can occur is m × n. Extend this principle to all positions on the license plate.
Step 3: Calculate the number of possibilities for the letters. Since there are three letters and each can be chosen independently, the total number of combinations for the letters is 26 × 26 × 26 (or 26^3).
Step 4: Calculate the number of possibilities for the digits. Since there are four digits and each can be chosen independently, the total number of combinations for the digits is 10 × 10 × 10 × 10 (or 10^4).
Step 5: Multiply the total number of combinations for the letters by the total number of combinations for the digits to find the total number of possible license plates. This is (26^3) × (10^4).

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Key Concepts

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

Fundamental Counting Principle

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second independent event can occur in 'n' ways, then the total number of ways both events can occur is 'm × n'. This principle is essential for calculating the total combinations of outcomes in scenarios involving multiple independent choices.
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Fundamental Counting Principle

Permutations and Combinations

Permutations refer to the arrangement of items where the order matters, while combinations refer to the selection of items where the order does not matter. In the context of license plates, since the arrangement of letters and digits is significant, we focus on permutations to determine the total possible configurations.
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Counting Outcomes

Counting outcomes involves determining the total number of possible results in a given scenario. For the Virginia license plates, we calculate the number of choices for letters (26 options for each of the three letters) and digits (10 options for each of the four digits), and then multiply these choices to find the total number of unique license plates.
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Related Practice
Textbook Question

In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

11. The probability of rolling 2 six-sided dice and getting a sum of 9 is 1/9.

Textbook Question

In Exercises 33 and 34, use the pie chart at the left, which shows the percent distribution of the number of students in U.S. public schools in a recent year. (Source: U.S. National Center for Education Statistics)

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34. Find the probability of randomly selecting a school with 300 or more students.

Textbook Question

"In Exercises 17 and 18, use the table, which shows the numbers of first-time and repeat U.S. nursing students taking the National Council Licensure Examination (NCLEX-RN® exam) to pass or fail in a recent year. (Adapted from National Council Licensure Examinations)

18. Find the probability that a student passed, given that the student repeated the exam."

Textbook Question

28. A sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans. Find the probability that a randomly chosen automobile from this sample is black or a sedan.

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Textbook Question

In Exercises 49-53, use counting principles to find the probability.

53. A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is the

probability of choosing

b. four women?

Textbook Question

"In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.

20. Selecting an ace from a standard deck of 52 playing cards, and then selecting a jack from the deck without replacing the ace"