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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

A box contains 10 red marbles and 10 green marbles. a. Sampling at random from the box five times with replacement, you have drawn a red marble all five times. What is the probability of drawing a red marble the sixth time? b. Sampling at random from the box five times without replacement, you have drawn a red marble all five times. Without replacing any of the marbles, what is the probability of drawing a red marble the sixth time? c. You have tossed a fair coin five times and have obtained heads all five times. A friend argues that according to the law of averages, a tail is due to occur and, hence, the probability of obtaining a head on the sixth toss is less than \(.50 .\) Is he right? Is coin tossing mathematically equivalent to the procedure mentioned in part a or the procedure mentioned in part b? Explain.

A test contains two multiple-choice questions. If a student makes a random guess to answer each question, how many outcomes are possible? Depict all these outcomes in a Venn diagram. Also draw a tree diagram for this experiment. (Hint: Consider two outcomes for each question- either the answer is correct or it is wrong.)

The probability of a student getting an A grade in an economics class is \(.24\) and that of getting a B grade is \(.28\). What is the probability that a randomly selected student from this class will get an \(\mathrm{A}\) or a \(\mathrm{B}\) in this class? Explain why this probability is not equal to \(1.0\)

A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is \(\begin{array}{ll}\text { a. red? } & \text { b. green? }\end{array}\)

Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses. $$\begin{array}{lcc} \hline & \text { Have Shopped } & \text { Have Never Shopped } \\ \hline \text { Male } & 500 & 700 \\ \text { Female } & 300 & 500 \end{array}4$ a. If one adult is selected at random from these 2000 adults, find the probability that this adult i. has never shopped on the Internet ii. is a male iii. has shopped on the Internet given that this adult is a female iv. is a male given that this adult has never shopped on the Internet b. Are the events "male" and "female" mutually exclusive? What about the events "have shopped" and "male?" Why or why not? c. Are the events "female" and "have shopped" independent? Why or why not?
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