Textbook Question
ESP A psychologist tells you that in an ESP (extrasensory perception) experiment, there is a 20% chance of answering a question correctly. What is the probability of answering a question correctly?
Ch. 4 - Probability
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Chapter 4, Problem 4.q.8
In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.
If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 who had the vaccine treatment and developed flu.
Verified step by step guidance1
Step 1: Identify the total number of subjects in the experiment. Add all the values in the table: 14 (Vaccine Treatment, Developed Flu) + 1056 (Vaccine Treatment, Did Not Develop Flu) + 95 (Placebo, Developed Flu) + 437 (Placebo, Did Not Develop Flu).
Step 2: Focus on the specific group mentioned in the problem: subjects who had the vaccine treatment and developed flu. From the table, this corresponds to the value 14.
Step 3: Calculate the probability by dividing the number of subjects in the specified group (14) by the total number of subjects (calculated in Step 1). Use the formula: \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
Step 4: Express the probability in decimal form. Ensure the division result is converted to a decimal.
Step 5: Verify the calculation by double-checking the values from the table and ensuring the probability is correctly expressed in decimal form.
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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 refers to the chance of randomly selecting a subject who received the vaccine treatment and developed flu. The probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes.
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Favorable Outcomes
Favorable outcomes are the specific results that we are interested in when calculating probability. In this case, the favorable outcome is the number of subjects who received the vaccine treatment and developed flu, which is 14. Understanding favorable outcomes is crucial for accurately determining the probability of an event.
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Guided course
06:00The Binomial Experiment
Total Outcomes
Total outcomes refer to the complete set of possible results in a probability scenario. Here, the total number of subjects is 1602, which includes both those who received the vaccine and those who received the placebo. Knowing the total outcomes is essential for calculating the probability, as it serves as the denominator in the probability formula.
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Related Practice
Textbook Question
Standard Tests Standard tests, such as the SAT or ACT or MCAT, tend to make extensive use of multiple-choice questions because they are easy to grade using software. If one such multiple choice question has possible correct answers of a, b, c, d, e, what is the probability of a wrong answer if the answer is a random guess?
Textbook Question
Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.
d. The probability that at least one of the children is a girl.
Textbook Question
Sampling Eye Color Based on a study by Dr. P. Sorita Soni at Indiana University, assume that eye colors in the United States are distributed as follows: 40% brown, 35% blue, 12% green, 7% gray, 6% hazel.
d. If two people are randomly selected, what is the probability that at least one of them has brown eyes?
Textbook Question
Subjective Probability Estimate the probability that the next time you watch a TV news report, it includes a story about a plane crash.
Textbook Question
In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.
If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 that developed flu.