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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
Chapter 4, Problem 4.4.18

Teed Off When four golfers are about to begin a game, they often toss a tee to randomly select the order in which they tee off. What is the probability that they tee off in alphabetical order by last name?

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Step 1: Understand the problem. The goal is to calculate the probability that four golfers tee off in alphabetical order by last name. This involves determining the total number of possible orders and identifying the specific order that matches the alphabetical arrangement.
Step 2: Calculate the total number of possible orders. Since there are four golfers, the number of ways they can be arranged is given by the factorial of 4, denoted as 4!. The formula for factorial is n! = n × (n-1) × (n-2) × ... × 1. For 4 golfers, this would be 4 × 3 × 2 × 1.
Step 3: Identify the favorable outcome. There is only one specific arrangement where the golfers tee off in alphabetical order by last name. This is the favorable outcome.
Step 4: Calculate the probability. The probability of an event is given by the formula P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes). Substitute the values: the number of favorable outcomes is 1, and the total number of possible outcomes is 4!.
Step 5: Simplify the expression. To find the probability, simplify the fraction using the value of 4! calculated earlier. This will give the final probability that the golfers tee off in alphabetical order by last name.

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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 this context, it quantifies the chance of the golfers teeing off in a specific order, which can be calculated by considering all possible arrangements of the golfers.
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Permutations

Permutations refer to the different ways in which a set of items can be arranged in order. For four golfers, the total number of permutations is calculated as 4! (4 factorial), which equals 24. This concept is essential for determining the total possible outcomes when arranging the golfers.
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Favorable Outcomes

Favorable outcomes are the specific outcomes that satisfy the condition of interest—in this case, the golfers teeing off in alphabetical order. Since there is only one specific arrangement that meets this criterion among the total permutations, understanding favorable outcomes is crucial for calculating the probability.
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Related Practice
Textbook Question

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Texting and Alcohol If one of the high school drivers is randomly selected, find the probability that the selected driver did not text while driving and did not drive when drinking.

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Textbook Question

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.



Voting Repeat the preceding Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 26 Democrats being placed on the first line. The probability of getting a result as high as 26 is 0.058638.

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Textbook Question

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.



Movies Based on a study of the movies made in a recent year, 33 out of every 100 movies have a female lead or co-lead.

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Textbook Question

In Exercises 29–32, use the given sample space or construct the required sample space to find the indicated probability.



Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 2): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

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Textbook Question

In Exercises 29–32, use the given sample space or construct the required sample space to find the indicated probability.



Four Children Exercise 29 lists the sample space for a couple having three children. After identifying the sample space for a couple having four children, find the probability of getting three girls and one boy (in any order).

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Textbook Question

Quinela In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 144th running of the Kentucky Derby had a field of 20 horses. What is the probability of winning a quinela bet if you randomly select the horses?

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