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# PSY 2110, Probability Notes (Week 4) 2110

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This 3 page Class Notes was uploaded by Madie Ritter on Monday September 26, 2016. The Class Notes belongs to 2110 at Ohio University taught by S. Tice-Alicke in Fall 2016. Since its upload, it has received 17 views. For similar materials see PSY 2110 (Behavioral Statistics) in Psychology at Ohio University.

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Date Created: 09/26/16

Week 4 PROBABILITY An assertion about how likely it is that a particular event or relationship will occur 1. VIEWS OF PROBABILITY A. Analytic View An analysis of possible outcomes to define probability i. P (A) = A/A+B ii. Answers will be between 0 and 1 iii. i.e. P (having a boy) =1/2=.5 B. Relative Frequency View Defines probability in terms of past performance/outcomes i. i.e. 1. number of girls in a county: 652 2. number of boys in a county: 645 a. therefore, P (having a boy) =645/645+652= 645/1,297= . 4973 C. Subjective View Not based on actual numbers or calculations; it is defined in terms of personal belief in an outcome’s likelihood i. This view of probability may not always be accurate but it is important because it influences our behavior ii. i.e. your subjective view of how a date may go will influence your confidence 2. BASIC TERMINOLOGY RELATING TO PROBABILITY A. Event: the “thing” whose probability we are calculating B. Independent Events: the occurrence of one event has no effect on the probability of the occurrence of the other i. i.e. gender, rolling a dice C. Mutually Exclusive Events: the occurrence of one event precludes (makes impossible) the occurrence of the other i. i.e. days of the week (if it is Monday it cannot be Tuesday) 3. BASIC LAWS OF PROBABILITY A. 0 ≤ P(A) ≥ 1 For any event (A), the probability of A occurring is between 0 and 1 i. With 0 corresponding to no chance of the event occurring and 1 corresponding to definite occurrence B. Additive Law i. Used for mutually exclusive events only ii. P (A or B) = P(A) + P(B) iii. Since a standard deck of cards is often referenced in problems dealing with this law, it is important to remember that a standard deck of cards holds 52; 13 of each suit. iv. i.e. P(drawing an ace or a king) = P(Ace) + P(King) = 4/52 + 4/52 = 8/52 = .1538 C. Multiplication Law i. If two events are independent, the probability of both of them occurring together is the product of their separate probabilities ii. P (A and B) = P (A,B) = P(A) x P(B) iii. It is important that, when dealing with the multiplication rule, you take note of if the drawings occur with replacement or not. 1. If the problem does not occur with replacement, the events are not independent and therefore cannot be used with the multiplication rule 4. TYPES OF PROBABILITY A. Joint: the probability of the co-occurrence of 2 or more events, P (A,B) i. If said events are independent, the multiplication law can be applied B. Conditional: the probability that one event will occur given that some other event has occurred, P (A/B) i. Probability of A, given B ii. Used for dependent events iii. i.e. Republicans Democrats Pro-Nuclear 70 10 Anti-Nuclear 30 80 1. Find the probability that a person is republican and anti- nuclear: 2 a. First, find the slot that possess both characteristics and use this number for the numerator; 30. For the denominator, use the total number of people, 190. b. 30/190= .1579 2. Find the probability that a person was pro-nuclear, given that they are republican: a. First, fine the slot that possess both characteristics and use this number for the numerator; 70. For the denominator, find the total a=of the two categories that are unknown, whether the person is pro-nuclear or anti- nuclear; 100. b. 70/100= .7 3

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