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Chapter 6: Problem 1

Define the term chance experiment, and give an example of a chance experiment with four possible outcomes.

Short Answer

Expert verified
A Chance Experiment refers to a procedure that results in one or more uncertain outcomes. An example of a chance experiment with four possible outcomes is rolling a four-sided die. The results could be 1, 2, 3, or 4.

Step by step solution

01

Define Chance Experiment

A Chance Experiment is a mathematical term relating to probability. It's an action or procedure that results in one or several outcomes, where the outcome is uncertain. In other words, it is possible to note all possible outcomes, but it is uncertain which particular outcome will happen.
02

Provide an Example

An example of a chance experiment with four possible outcomes could be rolling a four-sided die (also known as a D4 in gaming terms). When the die is rolled, it could result in four different outcomes: landing on 1, 2, 3, or 4.

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Most popular questions from this chapter

A bookstore sells two types of books (fiction and nonfiction) in several formats (hardcover, paperback, digital, and audio). For the chance experiment that consists of observing the type and format of a single-book purchase, two possible outcomes are a hardcover fiction book and an audio nonfiction book. a. There are eight outcomes in the sample space for this experiment. List these possible outcomes. b. Do you think it is reasonable to think that the outcomes for this experiment would be equally likely? Explain. c. For customers who purchase a single book, the estimated probabilities for the different possible outcomes are given in the cells of the accompanying table. What is the probability that a randomly selected single-book purchase will be for a book in print format (hardcover or paperback)? $$ \begin{array}{l|cccc} {\text { Hardcover }} & \text { Paperback } & \text { Digital } & \text { Audio } \\ \hline \text { Fiction } & .15 & .45 & .10 & .10 \\ \text { Nonfiction } & .08 & .04 & .02 & .06 \\ \hline \end{array} $$ d. Show two different ways to compute the probability that a randomly selected single-book purchase will be for a book that is not in a print format. e. Find the probability that a randomly selected singlebook purchase will be for a work of fiction.

The National Public Radio show Car Talk has a feature called "The Puzzler." Listeners are asked to send in answers to some puzzling questions-usually about cars but sometimes about probability (which, of course, must account for the incredible popularity of the program!). Suppose that for a car question, 800 answers are submitted, of which 50 are correct. a. Suppose that the hosts randomly select two answers from those submitted with replacement. Calculate the probability that both selected answers are correct. (For purposes of this problem, keep at least five digits to the right of the decimal.) b. Suppose now that the hosts select the answers at random but without replacement. Use conditional probability to evaluate the probability that both answers selected are correct. How does this probability compare to the one computed in Part (a)?

Only \(0.1 \%\) of the individuals in a certain population have a particular disease (an incidence rate of .001). Of th贸se wh貌 have the disease, \(95 \%\) test possitive wh猫n a certain diagnostic test is applied. Of those who do not have the disease, \(90 \%\) test negative when the test is applied. Suppose that an individual from this population is randomly selected and given the test. a. Construct a tree diagram having two first-generation branches, for has disease and doesn't have disease, and two second-generation branches leading out from each of these, for positive test and negative test. Then enter appropriate probabilities on the four branches. b. Use the general multiplication rule to calculate \(P\) (has disease and positive test). c. Calculate \(P\) (positive test). d. Calculate \(P\) (has disease| positive test). Does the result surprise you? Give an intuitive explanation for the size of this probability.

Consider the chance experiment in which the type of transmission-automatic (A) or manual (M) - is recorded for each of the next two cars purchased from a certain dealer. a. What is the set of all possible outcomes (the sample space)? b. Display the possible outcomes in a tree diagram. c. List the outcomes in each of the following events. Which of these events are simple events? i. \(B\) the event that at least one car has an automatic transmission ii. \(C\) the event that exactly one car has an automatic transmission iii. \(D\) the event that neither car has an automatic transmission d. What outcomes are in the event \(B\) and \(C ?\) In the event \(B\) or \(C\) ?

Suppose that a box contains 25 light bulbs, of which 20 are good and the other 5 are defective. Consider randomly selecting three bulbs without replacement. Let \(E\) denote the event that the first bulb selected is good, \(F\) be the event that the second bulb is good, and \(G\) represent the event that the third bulb selected is good. a. What is \(P(E)\) ? b. What is \(P(F \mid E)\) ? c. What is \(P(G \mid E \cap F)\) ? d. What is the probability that all three selected bulbs are good?
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