Textbook Question
Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.
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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 4.2.33
Exclusive Or The exclusive or means either one or the other event occurs, but not both.
If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.
b. Repeat Exercise 11 “Texting or Drinking” using the exclusive or instead of the inclusive or.
Verified step by step guidance1
Understand the concept of 'exclusive or': The exclusive or (XOR) means that either one event occurs or the other event occurs, but not both. This is different from the inclusive or, which allows for both events to occur simultaneously.
Identify the probabilities of the individual events: Let P(A) represent the probability of texting while driving, and P(B) represent the probability of driving when drinking alcohol. These probabilities should be provided in the problem or calculated from the data.
Identify the probability of both events occurring simultaneously: Let P(A ∩ B) represent the probability that a driver both texted while driving and drove when drinking alcohol. This value should also be provided or calculated from the data.
Apply the formula for the probability of the exclusive or: The formula for the exclusive or is P(A XOR B) = P(A) + P(B) - 2 * P(A ∩ B). This formula ensures that the overlap (both events occurring) is subtracted twice to exclude it entirely.
Substitute the known values into the formula: Replace P(A), P(B), and P(A ∩ B) with their respective values to calculate the probability of a driver who either texted while driving or drove when drinking alcohol, but not both.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exclusive Or (XOR)
The exclusive or (XOR) is a logical operation that results in true if and only if one of the operands is true, but not both. In probability, this means that when calculating the likelihood of two events, we consider only the scenarios where one event occurs without the other. For example, if we are looking at the events of texting while driving and drinking while driving, XOR would mean we are interested in cases where a driver either texted or drank, but not both.
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Probability of Mutually Exclusive Events
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 question, we are interested in calculating the probability of selecting a high school driver who either texted while driving or drove after drinking alcohol. This involves determining the number of favorable outcomes over the total number of possible outcomes.
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5:37Introduction to Probability
Mutually Exclusive Events
Mutually exclusive events are events that cannot occur at the same time. In the context of the exclusive or, if one event occurs, the other cannot. For instance, if a driver is texting while driving, they cannot simultaneously be drinking alcohol. Understanding this concept is crucial for correctly applying the XOR in probability calculations, as it simplifies the process of determining the total probability of either event occurring.
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Related Practice
Textbook Question
Notation For a polygraph (lie detector) used when a subject is presented with a question, let L= the subject lied and let Y = the polygraph indicated that the subject told a lie. Use your own words to translate the notation P (Y|L) into a verbal statement.
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Textbook Question
In Exercises 17–20, refer to the accompanying table showing results from experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known whether or not the subject lied, so the table indicates when the polygraph (lie detector) test was correct.
False Negative Find the probability of selecting a subject with a negative polygraph result, given that the subject lied. What would be an unfavorable consequence of this error?
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Textbook Question
Penicillin “Who discovered penicillin: Marcel Bich, William Penn, Jonas Salk, Alexander Fleming, or Louis Pasteur?” If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Alexander Fleming?
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Textbook Question
In Exercises 21-28, find the probability and answer the questions.
Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the expected value of as Mendel claimed?
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Textbook Question
Women in Movies In a recent year, speaking characters in movies were 68.2% male. What is the probability of randomly selecting a character with a speaking part and getting a female? What should be the value of that probability?
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