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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 4 - Probability문제 4.1.42a
4장, 문제 4.1.42a

Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number.


a. What is your probability of winning?

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Step 1: Understand the problem. A roulette wheel has 38 slots: 1 slot is 0, 1 slot is 00, and the remaining 36 slots are numbered 1 through 36. You are betting on the outcome being an odd number. To calculate the probability of winning, we need to determine how many odd numbers are present and divide that by the total number of slots.
Step 2: Identify the odd numbers. The numbers 1 through 36 alternate between odd and even. Therefore, half of these numbers are odd. Calculate the total number of odd numbers as \( \frac{36}{2} = 18 \).
Step 3: Determine the total number of possible outcomes. Since the roulette wheel has 38 slots, the total number of possible outcomes is 38.
Step 4: Calculate the probability of winning. The probability of an event is given by the formula \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Substitute the values: \( P(\text{odd number}) = \frac{18}{38} \).
Step 5: Simplify the fraction if needed. If the fraction \( \frac{18}{38} \) can be reduced, simplify it to its lowest terms to express the probability in its simplest form.

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주요 개념

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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 roulette, it is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you want to find the probability of landing on an odd number, you would count the odd numbers on the wheel and divide that by the total slots.
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Introduction to Probability

Favorable Outcomes

Favorable outcomes refer to the specific results that align with the event of interest. In the case of betting on an odd number in roulette, the favorable outcomes are the odd-numbered slots on the wheel. Understanding how many favorable outcomes exist is crucial for calculating the probability of winning your bet.
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The Binomial Experiment

Total Outcomes

Total outcomes represent all possible results that can occur in a given scenario. In roulette, the total outcomes are the 38 slots on the wheel, which include numbers 1 through 36, 0, and 00. Knowing the total number of outcomes is essential for determining the probability of any event, including the likelihood of landing on an odd number.
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Fundamental Counting Principle
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Identity Theft with Credit Cards Credit card numbers typically have 16 digits, but not all of them are random.


a. What is the probability of randomly generating 16 digits and getting your MasterCard number?


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Kentucky Derby Odds When the horse Justify won the 144th Kentucky Derby, a \$2 bet on a Justify win resulted in a winning ticket worth \(7.80.


a. How much net profit was made from a \)2 win bet on Justify?

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교과서 질문

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive (incorrect) results; among 157 negative results, there are 3 false negative (incorrect) results. (Hint: Construct a table similar to Table 4-1.)


Testing for Marijuana Use


a. How many subjects are included in the study?

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Denomination Effect

In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters versus a \$1 bill, some college students were given four quarters and others were given a \$1 bill, and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).



Denomination Effect


a. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

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ATM You want to obtain cash by using an ATM, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.


a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly?

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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 three of the high school drivers are randomly selected from the 4720 subjects who did not text while driving, find the probability that all three drove when drinking.


a. Assume that the selections are made with replacement. Are the events independent?

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