Chapter 7 Notes
Chapter 7 Notes PSY 2110
Popular in Statistics for Behavioral Sciences
Popular in Psychology (PSYC)
This 4 page Class Notes was uploaded by Shannan Dillen on Monday September 26, 2016. The Class Notes belongs to PSY 2110 at Ohio University taught by S. Tice-Alicke in Fall 2016. Since its upload, it has received 51 views. For similar materials see Statistics for Behavioral Sciences in Psychology (PSYC) at Ohio University.
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Date Created: 09/26/16
Chapter 7: Basic Concepts of Probability Probability – an assertion about how likely it is that a particular event or relationship will occur Views of Probability 1. Analytical View: An analysis of possible outcomes to define probability Ex: A bag contains 1 black marble and 9 white marbles. What is the probability of drawing a black marble? P(A) = A / (A + B) if event could be A or B and all outcomes are equally likely *Reduce to decimal form* -4 decimal places Ex: p(baby boy) = ½ = .5 1 choice / 2 possibilities 2. Relative Frequency View: Defines probability in terms of past performance/outcomes. Ex: Waiting for a bus and after many days of doing this you notice that 75/100 times the bus is late. P(bus late) = .75 Ex: P(boy) in Athens county? Girls in county = 652 Boys in county = 645 P(boy) = 645 / (645 + 652) = .4973 3. Subjective View: Not based on actual numbers or calculations; defined in terms of personal belief in an outcome’s likelihood *may not be accurate, but it’s important because it influences our behavior Ex: weather, likelihood of rejection if we ask someone out, likelihood of being punished if committing a crime Basic Terminology Event – basic bit of data – “thing” whose probability we are calculating – any kind of outcome 1. Independent Events The occurrence of one event has no effect on the probability of the occurrence of the other. -no cause-effect relationship Ex: dice rolls, knowing first child born in a year is a boy is independent of what gender the second child born that year will be 2. Mutually Exclusive Events The occurrence of one event precludes (makes impossible) to occurrence of the other -if it’s one, it can’t be the other -outcomes cannot occur simultaneously Ex: gender, days of the week, when you roll a die it is impossible to roll both a 3 and a 5 Basic Laws of Probability 1. 0 < p(A) < 1 For any event (A), the probability of A occurring is between 0 and 1. (0 = no chance whatsoever. Ex: p(tail) on a 2-headed coin) (1 = definite occurrence. Ex: p(heads) on a 2-headed coin) 2. Additive Law (addition rule of probability) We use: additive law: for mutually exclusive events only P(A or B) = p(A) + p(B) Ex: p(ace or king) = p(ace) + p(king) 4/52 + 4/52 = 8/52 = .1538 Ex: in rolling a fair die once, what is the probability of rolling a 1 or an even number? P(one or even) = p(one) + p(even) 1/6 + 3/6 = 4/6 = 2/3 = .6667 Ex: 130 people 40 children, 60 teens, 30 adults P(teen or adult) = p(teen) + p(adult) 60/130 + 30/130 = 90/130 = .6923 3. Multiplication Rule If 2 events are independent, the probability of both of them occurring together is the product of their separate probabilities. P(A and B) = p(A) * p(B) = p(A,B) Ex: flip a pair of pennies once P(head, head) = p(head) * p(head) ½ * ½ = .25 Ex: roll pair of fair die once P(2 on die 1, 4 one die 2) = p(2) * p(4) = 1/6 * 1/6 = .0278 Ex: 110 people 50 men, 60 women P( woman on first, woman on second) = 60/110 * 60/110 = .2975 Types of Probability (aside from single event) Joint – probability of co-occurrence of z or more events p(A,B) *if independent, can we use multiplication rule to compute Conditional Probability – probability that one event will occur given that some other event has occurred P(A/B): probability of A given B; probability of A if B is true (non-independent events) Ex: Take a survey of political parties and nuclear power preferences. (190 total people surveyed) Republican Democrat Pro-nuclear 70 10 Anti-nuclear 30 80 Find probability that: 1. Person was Rep. and anti-nuclear 30/190 = .1579 2. Person was pro-nuclear, given Rep. 70/100 = .7000 3. Person was Dem., given anti-nuclear P(D/an) = 80/110 = .7273 4. Person was pro-nuclear, given Dem. P(pn/D) = 10/90 = .1111
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