Stats chapter 4 Exam Review

A sample space is the set of all possible outcomes of a probability experiment.

Define sample space.

0

If an event cannot happen, what value is assigned to its probability?

P(R) = 1 - 0.20 = 0.80 or 80% chance that it will not rain. I would not take an umbrella.

If the probability that it will rain tomorrow is 0.20, what is the probability that it won't rain tomorrow? Would you recommend taking an umbrella?

Equally likely events are events that have the same probability of occurring.

What are equally likely events?

A probability experiment is a chance process that leads to well-defined outcomes.

What is a probability experiment?

An outcome is the result of a single trial of a probability experiment, but an event can consist of more than one outcome.

What is the difference between an outcome and an event?

The range of values is 0 to 1 inclusive.

What is the range of the values of the probability of an event?

1

What is the sum of the probabilities of all the outcomes in a sample space?

1

When an event is certain to occur, what is its probability?

Classical probability uses sample spaces to determine the numerical probability that an event will happen. You do not actually have to perform the experiment to determine that probability. Classical probability is so named because it was the first type of probability studied formally by mathematicians in the 17th and 18th centuries. *Classical probability assumes that all outcomes in the sample space are equally likely to occur.* For example, when a single die is rolled, each outcome has the same probability of occurring. Since there are six outcomes, each outcome has a probability of . When a card is selected from an ordinary deck of 52 cards, you assume that the deck has been shuffled, and each card has the same probability of being selected. In this case, it is .

Define classical probability

-3/5, 1.65, -0.44, 125%

A probability experiment is conducted. Which of these *cannot* be considered a probability of an outcome? 2/3 0.63 -3/5 1.65 −0.44 0 1 125% 24%

empirical

Classify each statement as an example of classical probability, empirical probability, or subjective probability. a. The probability that a person will watch the 6 o'clock evening news is 0.15.

classical

Classify each statement as an example of classical probability, empirical probability, or subjective probability. b. The probability of winning at a Chuck-a-Luck game is 5/36.

empirical

Classify each statement as an example of classical probability, empirical probability, or subjective probability. c. The probability that a bus will be in an accident on a specific run is about 6%.

classical

Classify each statement as an example of classical probability, empirical probability, or subjective probability. d. The probability of getting a royal flush when five cards are selected at random is __________________

The difference between classical and empirical probability is that classical probability assumes that certain outcomes are equally likely (such as the outcomes when a die is rolled), while empirical probability relies on actual experience to determine the likelihood of outcomes. In empirical probability, one might actually roll a given die 6000 times, observe the various frequencies, and use these frequencies to determine the probability of an outcome. Suppose, for example, that a researcher for the American Automobile Association (AAA) asked 50 people who plan to travel over the Thanksgiving holiday how they will get to their destination. The results can be categorized in a frequency distribution as shown.

Define empirical probability

The third type of probability is called subjective probability. *Subjective probability uses a probability value based on an educated guess or estimate, employing opinions and inexact information.* In subjective probability, a person or group makes an educated guess at the chance that an event will occur. This guess is *based on the person's experience and evaluation of a solution.* For example, a sportswriter may say that there is a 70% probability that the Pirates will win the pennant next year. A physician might say that, on the basis of her diagnosis, there is a 30% chance the patient will need an operation. A seismologist might say there is an 80% probability that an earthquake will occur in a certain area. These are only a few examples of how subjective probability is used in everyday life. All three types of probability (classical, empirical, and subjective) are used to solve a variety of problems in business, engineering, and other fields

Define subjective probability