Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.2.5

Chapter 4, Problem 4.2.5

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?

Verified step by step guidance

Step 1: Understand the problem. The problem states that 68.2% of speaking characters in movies are male. To find the probability of selecting a female character, we need to calculate the complement of the probability of selecting a male character.

Step 2: Recall the complement rule in probability. The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. Mathematically, this can be expressed as:

P(\(\text{Female}\)) = 1 - P(\(\text{Male}\))

Step 3: Substitute the given probability of selecting a male character into the formula. The problem states that

P(\(\text{Male}\)) = 0.682

. Using the complement rule, substitute this value into the formula:

P(\(\text{Female}\)) = 1 - 0.682

Step 4: Perform the subtraction to find the probability of selecting a female character. This step involves calculating

1 - 0.682

, which will give the probability of selecting a female character.

Step 5: Interpret the result. The resulting probability represents the likelihood of randomly selecting a speaking character in movies and getting a female. Ensure the final probability is expressed as a decimal or percentage, depending on the context.

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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 female character from a group of speaking characters in movies. The probability can be calculated by dividing the number of favorable outcomes (female characters) by the total number of possible outcomes (all speaking characters).

Complementary Events

Complementary events are pairs of outcomes that cover all possible scenarios of a given situation. In this case, the probability of selecting a female character is the complement of selecting a male character. Since 68.2% of speaking characters are male, the probability of selecting a female character can be found by subtracting the probability of selecting a male from 1, which highlights the relationship between these two outcomes.

Percentage to Probability Conversion

Converting percentages to probabilities is essential for statistical analysis. A percentage represents a part of a whole, while probability quantifies the chance of an event occurring. To find the probability of selecting a female character, one must first convert the percentage of male characters (68.2%) into a decimal (0.682) and then use this value to determine the probability of selecting a female character, which is 1 - 0.682.

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Introduction to Probability

Related Practice

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.

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.

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?

Textbook Question

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.

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?

Textbook Question

Mendel’s Peas Mendel conducted some of his famous experiments with peas that were either smooth yellow plants or wrinkly green plants. If four peas are randomly selected from a batch consisting of four smooth yellow plants and four wrinkly green plants, find the probability that the four selected peas are of the same type.