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Ch. 5 - Discrete Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 5 - Discrete Probability DistributionsProblem 5.1.29b
Chapter 5, Problem 5.1.29b

Expected Value for the Florida Pick 3 Lottery In the Florida Pick 3 lottery, you can bet \$1 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect \$500.


b. What is the probability of winning?

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Step 1: Understand the problem. In the Florida Pick 3 lottery, you are selecting a sequence of three digits (e.g., 123). Each digit can range from 0 to 9, and the order of the digits matters. To win, your chosen sequence must match the winning sequence exactly.
Step 2: Calculate the total number of possible outcomes. Since each digit has 10 possible values (0 through 9), and there are three digits, the total number of possible outcomes is given by the formula for permutations with repetition: 103. This represents the total number of unique three-digit combinations.
Step 3: Determine the number of favorable outcomes. There is only one favorable outcome: the specific sequence of three digits you selected that matches the winning sequence exactly.
Step 4: Calculate the probability of winning. Probability is defined as the ratio of favorable outcomes to total outcomes. Use the formula: 1103. This represents the likelihood of your chosen sequence being the winning sequence.
Step 5: Simplify the probability expression. Simplify the fraction to express the probability in its simplest form. This will give you the final probability of winning the Florida Pick 3 lottery.

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Key Concepts

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

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of the Florida Pick 3 lottery, the probability of winning is calculated by determining the number of favorable outcomes (matching the drawn numbers) divided by the total number of possible outcomes (all combinations of three digits from 0 to 9).
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Combinatorics

Combinatorics is a branch of mathematics dealing with combinations and arrangements of objects. For the Florida Pick 3 lottery, it helps in calculating the total number of possible combinations of three digits, which is essential for determining the probability of winning. Since each digit can be any number from 0 to 9, the total combinations are 10 x 10 x 10, or 1,000.

Expected Value

Expected value is a key concept in statistics that represents the average outcome of a random event when considering all possible outcomes and their probabilities. In the case of the Florida Pick 3 lottery, the expected value can be calculated by multiplying the probability of winning by the payout and subtracting the cost of the bet, providing insight into the game's potential profitability.
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Related Practice
Textbook Question

Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.


b. Find the probability of exactly 40 first lines for Democrats.

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Textbook Question

Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.


Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions.


c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?

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Textbook Question

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).


Using Probabilities for Significant Events


b. Find the probability of getting 2 or more matches.


Textbook Question

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).


Using Probabilities for Significant Events


b. Find the probability of getting 3 or more matches.

Textbook Question

In Exercises 25–28, find the probabilities and answer the questions.



Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability.


b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.


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Textbook Question

Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.


b. Among those who negotiated salary, 84% received higher pay. How many received higher pay?


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