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Chapter 4: Problem 17

Briefly explain the three approaches to probability. Give one example of each approach.

Short Answer

Expert verified
The three approaches to probability are the classical (assumes all outcomes are equally likely, e.g. rolling a dice), the relative frequency (based on experimental results, e.g. flipping a coin a certain number of times), and the subjective approach (based on personal belief or intuition, e.g. forecasting the weather).

Step by step solution

01

Classical Approach

The classical approach to probability is used when all the outcomes are equally likely. It assumes that it is possible to list all the experiment outcomes and none of those outcomes is favored over the others. A simple example of the classical probability is the tossing of a fair dice. There are six equally likely outcomes when a die is tossed, therefore, the probability of a number (for instance 1) appearing on the top face of the die is 1/6, counted as '1 favorable outcome' divide '6 total outcomes'.
02

Relative Frequency Approach

The relative frequency approach is based on experimental or empirical results. This approach defines the probability of an event as the ratio of the number of times the event occurred to the total number of trials. For instance, if a coin is flipped 100 times and it lands on heads 55 times, the relative frequency probability of the coin landing on heads is 55/100 = 0.55.
03

Subjective Approach

The subjective approach to probability enables quantification of uncertain events. It defines probability as a degree of belief, usually based on an individual's experience or intuition. For instance, a weather forecaster might predict a 70% chance of rain tomorrow, despite the lack of certain knowledge. The subjective probability in this case is 0.7.

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Most popular questions from this chapter

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.

Thirty-two persons have applied for a security guard position with a company. Of them, 7 have previous experience in this area and 25 do not. Suppose one applicant is selected at random. Consider the following two events: This applicant has previous experience, and this applicant does not have previous experience. If you are to find the probabilities of these two events, would you use the classical approach or the relative frequency approach? Explain why.

Which of the following values cannot be probabilities of events and why? \(\begin{array}{llllllll}1 / 5 & .97 & -.55 & 1.56 & 5 / 3 & 0.0 & -2 / 7 & 1.0\end{array}\)

What is meant by two mutually exclusive events? Give one example of two mutually exclusive events and another example of two mutually nonexclusive events.

In a sample survey, 1800 senior citizens were asked whether or not they have ever been victimized by a dishonest telemarketer. The following table gives the responses by age group. $$\begin{array}{l|llcc} & & & \begin{array}{c} \text { Have Been } \\ \text { Victimized } \end{array} & \begin{array}{c} \text { Have Never } \\ \text { Been Victimized } \end{array} \\ \hline & 60-69 & \text { (A) } & 106 & 698 \\ \text { Age } & 70-79 & \text { (B) } & 145 & 447 \\ & 80 \text { or over (C) } & 61 & 343 \\ \hline \end{array}$$ Suppose one person is randomly selected from these senior citizens. Find the following probabilities a. \(P(\) have been victimized or \(\mathrm{B}\) ) b. \(P(\) have never been victimized or \(\mathrm{C}\) )
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