Three Conceptual Approaches to Probability

The three conceptual approaches to probability are (1) classical probability, (2) the relative frequency concept of probability, and (3) the subjective probability concept.

Classical Probability

Many times, various outcomes for an experiment may have the same probability of occurrence.

Such outcomes are called equally likely outcomes. The classical probability rule is applied to

compute the probabilities of events for an experiment for which all outcomes are equally.

Definition

Equally Likely Outcomes Two or more outcomes (or events) that have the same probability of

occurrence are said to be equally likely outcomes (or events).

According to the classical probability rule, the probability of a simple event is equal to 1

divided by the total number of outcomes for the experiment. This is obvious because the sum

of the probabilities of all final outcomes for an experiment is 1, and all the final outcomes are

equally likely. In contrast, the probability of a compound event A is equal to the number of outcomes favorable to event A divided by the total number of outcomes for the experiment

Relative Frequency Concept of Probability

Suppose we want to calculate the following probabilities.

1. The probability that the next car that comes out of an auto factory is a "lemon"

2. The probability that a randomly selected family owns a home

3. The probability that a randomly selected woman has never smoked

4. The probability that an 80-year-old person will live for at least 1 more year

5. The probability that the tossing of an unbalanced coin will result in a head

6. The probability that a randomly selected person owns a sport-utility vehicle (SUV)

Although the various outcomes for each of these experiments are not equally likely, each of

these experiments can be performed again and again to generate data. In such cases, to calculate

probabilities, we either use past data or generate new data by performing the experiment a large

number of times. The relative frequency of an event is used as an approximation for the probability of that event. This method of assigning a probability to an event is called the relative frequency concept of probability. Because relative frequencies are determined by performing an experiment, the probabilities calculated using relative frequencies may change almost each time an experiment is repeated.

Subjective Probability

Many times we face experiments that neither have equally likely outcomes nor can be repeated

to generate data. In such cases, we cannot compute the probabilities of events using the classical

probability rule or the relative frequency concept. For example, consider the following probabilities of events:

1.The probability that Carol, who is taking a statistics course, will earn an A in the course

2. The probability that the Dow Jones Industrial Average will be higher at the end of the next

trading day

3. The probability that the New York Giants will win the Super Bowl next season

4. The probability that Joe will lose the lawsuit he has filed against his landlord

QUESTIONS

APPLICATIONS (ASSIGNMENT)

1.Suppose a randomly selected passenger is about to go through the metal detector at JFK Airport in New York City. Consider the following two outcomes: The passenger sets off the metal detector, and the passenger does not set off the metal detector. Are these two outcomes equally likely? Explain why or why not. If you are to find the probability of these two outcomes, would you use the classical approach or the relative frequency approach? Explain why.

2.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.

3.The president of a company has a hunch that there is a .80 probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, relative frequency, or subjective probability? Explain why.

4.The coach of a college football team thinks that there is a .75 probability that the team will win the national championship this year. Is this a case of classical, relative frequency, or subjective probability? Explain why.

5.A company that plans to hire one new employee has prepared a final list of six candidates, all of whom are equally qualified. Four of these six candidates are women. If the company decides to select at random one person out of these six candidates, what is the probability that this person will be a woman? What is the probability that this person will be a man? Do these two probabilities add up to 1.0? If yes, why?