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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

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 \(C\) ?

In a small city, approximately \(15 \%\) of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year. What is the probability that a particular eligible person in this city is selected in each of the next 2 years? In each of the next 3 years?

The article "Checks Halt over 200,000 Gun Sales" (San Luis Obispo Tribune, June \(5.2000\) ) reported that required background checks blocked 204,000 gun sales in \(1999 .\) The article also indicated that state and local police reject a higher percentage of would-be gun buyers than does the FBI, stating, "The FBI performed \(4.5\) million of the \(8.6\) million checks, compared with \(4.1\) million by state and local agencies. The rejection rate among state and local agencies was \(3 \%\), compared with \(1.8 \%\) for the FBI." a. Use the given information to estimate \(P(F), P(S)\), \(P(R \mid F)\), and \(P(R \mid S)\), where \(F=\) event that a randomly selected gun purchase background check is performed by the FBI, \(S=\) event that a randomly selected gun purchase background check is performed by a state or local agency, and \(R=\) event that a randomly selected gun purchase background check results in a blocked sale. b. Use the probabilities from Part (a) to evaluate \(P(S \mid R)\), and write a sentence interpreting this value in the context of this problem.

The article "Anxiety Increases for Airline Passengers After Plane Crash" (San Luis Obispo Tribune. November 13,2001 ) reported that air passengers have a 1 in 11 million chance of dying in an airplane crash. This probability was then interpreted as "You could fly every day for 26,000 years before your number was up." Comment on why this probability interpretation is misleading.

The newspaper article "Folic Acid Might Reduce Risk of Down Syndrome" (USA Today, September 29 . 1999) makes the following statement: "Older women are at a greater risk of giving birth to a baby with Down Syndrome than are younger women. But younger women are more fertile, so most children with Down Syndrome are born to mothers under \(30 . "\) Let \(D=\) event that a randomly selected baby is born with Down Syndrome and \(Y=\) event that a randomly selected baby is born to a young mother (under age 30 ). For each of the following probability statements, indicate whether the statement is consistent with the quote from the article, and if not, explain why not. a. \(P(D \mid Y)=.001, P\left(D \mid Y^{C}\right)=.004, P(Y)=.7\) b. \(P(D \mid Y)=.001, P\left(D \mid Y^{C}\right)=.001, P(Y)=.7\) c. \(P(D \mid Y)=.004, P\left(D \mid Y^{C}\right)=.004, P(Y)=.7\) d. \(P(D \mid Y)=.001, P\left(D \mid Y^{C}\right)=.004, P(Y)=.4\) e. \(P(D \mid Y)=.001, P\left(D \mid Y^{C}\right)=.001, P(Y)=.4\) f. \(P(D \mid Y)=.004, P\left(D \mid Y^{C}\right)=.004, P(Y)=.4\)
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