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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 a student graduating from Suburban State University has student loans to pay off after graduation is .60. The probability that a student graduating from this university has student loans to pay off after graduation and is a male is \(.24 .\) Find the conditional probability that a randomly selected student from this university is a male given that this student has student loans to pay off after graduation.

A random sample of 250 adults was taken, and they were asked whether they prefer watching sports or opera on television. The following table gives the two-way classification of these adults $$\begin{array}{lcc} \hline & \begin{array}{c} \text { Prefer Watching } \\ \text { Sports } \end{array} & \begin{array}{c} \text { Prefer Watching } \\ \text { Opera } \end{array} \\ \hline \text { Male } & 96 & 24 \\ \text { Female } & 45 & 85 \end{array}$$ a. If one adult is selected at random from this group, find the probability that this adult i. prefers watching opera ii. is a male iii. prefers watching sports given that the adult is a female iv. is a male given that he prefers watching sports \(\mathbf{v}\). is a female and prefers watching opera vi. prefers watching sports or is a male b. Are the events "female" and "prefers watching sports" independent? Are they mutually exclusive? Explain why or why not.

The probability that a randomly selected elementary or secondary school teacher from a city is a female is \(.68\), holds a second job is \(.38\), and is a female and holds a second job is \(.29\). Find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job.

Consider the following addition rule to find the probability of the union of two events \(A\) and \(B\) : $$P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)$$ When and why is the term \(P(A\) and \(B)\) subtracted from the sum of \(P(A)\) and \(P(B)\) ? Give one example where you might use this formula.

A company has installed a generator to back up the power in case there is a power failure. The probability that there will be a power failure during a snowstorm is \(.30\). The probability that the generator will stop working during a snowstorm is .09. What is the probability that during a snowstorm the company will lose both sources of power? Note that the two sources of power are independent.
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