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Chapter 4: Problem 18

Briefly explain for what kind of experiments we use the classical approach to calculate probabilities of events and for what kind of experiments we use the relative frequency approach.

Short Answer

Expert verified
The classical approach for probability is applied when all outcomes of an experiment are equally likely such as a dice roll. The relative frequency approach is used when the outcomes are not equally likely, such as predicting the weather.

Step by step solution

01

Identify the Classical Approach for Probability

The classical approach to probability is used when the outcomes of an experiment are equally likely. A common example would be a dice roll because each face (1 through 6) has the same chance of landing face up.
02

Identify the Relative Frequency Approach for Probability

The relative frequency approach requires greater historical data and is applied when the outcomes are not equally likely. For example, predicting the weather. Here the chance of getting rain versus sunshine isn't equally likely and will greatly depend on factors such as geographical location, season, and historical weather patterns.

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Most popular questions from this chapter

Given that \(A, B\), and \(C\) are three independent events, find their joint probability for the following a. \(P(A)=.49, \quad P(B)=.67\), and \(P(C)=.75\) b. \(P(A)=.71, \quad P(B)=.34\), and \(P(C)=.45\)

The probability that an open-heart operation is successful is .84. What is the probability that in two randomly selected open-heart operations at least one will be successful? Draw a tree diagram for this experiment.

Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two- way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same as, or worse off than their parents. $$\begin{array}{lccc} \hline & \begin{array}{c} \text { Less Than } \\ \text { High School } \end{array} & \begin{array}{c} \text { High } \\ \text { School } \end{array} & \begin{array}{c} \text { More Than } \\ \text { High School } \end{array} \\ \hline \text { Better off } & 140 & 450 & 420 \\ \text { Same as } & 60 & 250 & 110 \\ \text { Worse off } & 200 & 300 & 70 \\ \hline \end{array}$$ a. If one adult is selected at random from these 2000 adults, find the probability that this adult is i. financially better off than his/her parents ii. financially better off than his/her parents given he/she has less than high school education iii. financially worse off than his/her parents given he/she has high school education jy. financially the same as his/her parents given he/she has more than high school education b. Are the events "better off" and "high school" mutually exclusive? What about the events "less than high school" and "more than high school?" Why or why not? c. Are the events "worse off" and "more than high school" independent? Why or why not?

The probability that a randomly selected college student attended at least one major league baseball game last year is .12. What is the complementary event? What is the probability of this complementary event?

A student is to select three classes for next semester. If this student decides to randomly select one course from each of eight economics classes, six mathematics classes, and five computer classes, how many different outcomes are possible?
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