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Chapter 5

Department

PsychologyCourse Code

PSYB07H3Professor

Dwayne PareChapter

5This

**preview**shows pages 1-3. to view the full**17 pages of the document.**Textbook Notes PSYB07 September 28, 2016

Chapter #5 Lec 4

Chapter #5 – Basic Concepts of

Probability

5.1 – Probability

- The oldest and most common definition of probability is called the analytic view

-Analytic view: Definition of probability in terms of analysis of possible outcomes

oIf an event can occur in A ways and can fail to occur in B ways, and if all possible

ways are equally likely (e.g., each M&M in the bag has an equal chance of being

drawn), then the probability of its occurrence is A/(A 1 B), and the probability of

its failing to occur is B/(A 1 B).

oBecause there are 24 ways of drawing a blue M&M (one for each of the 24 blue

M&M’s in a bag of 100 M&M’s) and 76 ways of drawing a different color, A 5 24,

B 5 76, and p(A) 5 24/(24 1 76) 5 .24.

-Frequentist view

oSample with replacement: Sampling in which the item drawn on trial N is

replaced before the drawing on trial N + 1.

oIf we made a very large number of draws, we would find that (very nearly) 24%

of the draws would result in a blue M&M. Thus we might define probability as

the limit of the relative frequency of occurrence of the desired event that we

approach as the number of draws increases.

-Subjective probability: Definition of probability in terms of personal subjective belief in

the likelihood of an outcome.

oExample: “I think that tomorrow will be a good day,” is a subjective statement of

degree of belief, which probably has very little to do with the long-range relative

frequency of the occurrence of good days

oSubjective probabilities play an extremely important role in human decision-

making and govern all aspects of our behavior.

5.2 – Basic Terminology Rules

-Event: a term that statisticians use to cover just about anything

oThe occurrence of a king when we deal from a deck of cards, a score of 36 on a

scale of likeability, a classification of female for the next person appointed to

Supreme Court, the mean of a sample

oThe probability of “something”… that “something”= an event

-Independent events: when the occurrence or nonoccurrence of one has no effect on the

occurrence or nonoccurrence of the other

oThe voting behaviors of two randomly chosen subjects normally would be

assumed to be independent, especially with a secret ballot, because how one

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Textbook Notes PSYB07 September 28, 2016

Chapter #5 Lec 4

person votes could not be expected to influence how the other will vote.

othe voting behaviors of two members of the same family probably would not be

independent events, because those people share many of the same beliefs and

attitudes.

- Two events are said to be mutually exclusive if the occurrence of one event precludes

the occurrence of the other.

oFor example, the standard college classes of First Year, Sophomore, Junior, and

Senior are mutually exclusive because one person cannot be a member of more

than one class.

- A set of events is said to be exhaustive if it includes all possible outcomes.

oThus the four college classes in the previous example are exhaustive with respect

to full-time undergraduates, who have to fall in one or another of those

categories—if only to please the registrar’s office.

oAt the same time, they are not exhaustive with respect to total university

enrollments, which include graduate students, medical students,

nonmatriculated students, hangers-on, and so forth.

Basic Laws of Probability

- Two important theorems are central to any discussion of probability referred to as the

additive and multiplicative rules.

Additive Law of Probability

-additive law of probability: Given a set of mutually exclusive events, the probability of

the occurrence of one event or another is equal to the sum of their separate

probabilities.

oExample: M&Ms

probability that p(blue) = 24/100 = .24, p(green) = 16/100 = .16, and so

on.

Additive law: Thus, p(blue or green) = p(blue) + p(green) = .24 + .16 = .40.

The occurrence of one event precludes the occurrence of the other

If an M&M is blue, it can’t be green

Multiplicative Rule

-Multiplicative law of probability: The probability of the joint occurrence of two or more

independent events is the product of their individual probabilities.

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Textbook Notes PSYB07 September 28, 2016

Chapter #5 Lec 4

oExample: M&Ms

probability that p(blue) = 24/100 = .24, p(green) = 16/100 = .16, and

p(other) = .60

oMultiplicative law: Thus p(blue, blue) = p(blue) X p(blue) = .24 X .24 = .0576.

oSimilarly, the probability of a blue M&M followed by a green one is p(blue,

green) = p(blue) X p(green) = .24 X .16 = .0384.

Notice that we have restricted ourselves to independent events, meaning

the occurrence of one event can have no effect on the occurrence or

nonoccurrence of the other.

- Example: Race and death sentence

oWe need to calculate what this probability would be if the two events (race and

death sentence) are independent, as would be the case if verdicts are race-blind.

o If we assume that these two events are independent, the multiplicative law tells

us that p(nonwhite, death) = p(nonwhite) X p(death).

oIn their study 34.4% of the defendants were nonwhite, so the probability that a

defendant chosen at random would be nonwhite is .344.

oSimilarly, 8% of the defendants received a death sen- tence, giving p(death) = .

08.

oTherefore, if the two events are independent, p(nonwhite, death) = .344 X .08 = .

028 = 2.8%.

- Using both the additive law and multiplicative law:

oWhat is the probability that I will draw one blue M&M and one green M&M?

1st use the multiplicative rule ->

2nd use the additive rule ->

oThus the probability of obtaining one M&M of each of those colors over two

draws is approximately .08

- When to use the rules:

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