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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: Classical, which counts the favorable and total outcomes and assumes each outcome is equally likely; Frequency, which relies on historic data or repeated trials; Subjective, which involves personal judgment or estimation without set numerical values. Examples are rolling a dice for Classical, flipping a coin multiple times for Frequency, and predicting patient recovery by a doctor for Subjective.

Step by step solution

01

Classical Approach

The classical (also known as theoretical) approach to probability is often used when each outcome of an experiment is equally likely. This method considers the number of ways a specific event can happen and divides it by the total number of possible outcomes. For example, if you roll a fair six-sided die, the classical approach to probability can be used to calculate the probability of rolling a 3. Here, each outcome (1, 2, 3, 4, 5, 6) is equally likely. If we wanted to find the probability of rolling a 3, there is 1 way that this can happen (rolling a 3) and there are 6 possible outcomes. The probability is therefore \(\frac{1}{6}\).
02

Frequency (Empirical) Approach

The frequency (or empirical) approach is based on conducting a number of trials and recording the frequency of each outcome. The probability of an event happening is the frequency of the event occurring divided by the total number of trials. For instance, in flipping a coin 100 times, you might get 45 heads and 55 tails. Based on the frequency approach, the probability of getting heads is the number of heads divided by total flips, which is \(\frac{45}{100}\) = 0.45 or 45%.
03

Subjective Approach

The subjective approach to probability is based on a person's own judgement about the likelihood of an event happening. This approach is often used when there is lack of data or when it is impossible to perform all possible outcomes. For example, a doctor might use their experience and available medical knowledge to estimate the likelihood of a patient recovering from a disease. This likelihood will be the subjective probability.

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Most popular questions from this chapter

Explain the meaning of the intersection of two events. Give one example.

In a group of people, some are in favor of a tax increase on rich people to reduce the federal deficit and others are against it. (Assume that there is no other outcome such as "no opinion" and "do not know.") Three persons are selected at random from this group and their opinions in favor or against raising such taxes are noted. How many total outcomes are possible? Write these outcomes in a sample space \(S\). Draw a tree diagram for this experiment.

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

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