Probability Flashcards
What does probability do
helps assess the generalizability of data analysis
Gamblers fallacy
the incorrect belief that the probability of a particular event changes after a series of events has taken place
ex: thinking you’ll win if you double your cash with gambling
what is probability
the likelihood of something occurring
p(A) = # of outcomes classified as A/ total # of possible outcomes
ex: deck of cards
p(a spade) 13/52 = 1/4 = .25
p(king of hearts) = 1/52 = .019
views of probability
analytic - an analysis of possible outcomes to define probability
ex - bag contains 1 black marble and 9 green marbles. what is probability of drawing black marble
p(a) = a/a+b
relative frequency view
defines probability in terms of past performance/outcomes
waiting for a bus after many, many days of doing this you notice that 75/100 times the bus is late
subjective view
not based on actual numbers or calculations; probability defined in terms of personal belief in an outcomes likely make not be accurate
ex: likelihood of rejection is we ask someone on a date
event
the outcome of a trial
the thing whose probability we are calculating
independent events
events are independent when the occurrence of one event has no effect on the probability of occurrence of the other
2 things have no influence on each other
*dice rolls
mutually exclusive events
the occurrence of one event precludes (makes impossible) the occurrence of the other
*freshmen, sophomore, junior, senior
if it is one cannot be the other
exhaustive
the set of events that represents all possible outcomes
sample with replacement
item drawn of trial N is replaced
sample without replacement
the item drawn is not replaced before trial
non negative
between 1 and 0
the probability of A occurring is 1 and 0
if an event never occurs p(event) = 0
- p(tail) on a two headed coin
addition law (addition rule)
used when probability of two or more simple events is desired
-for mutually exclusive random events so idepenednat
p(a) + p(b)
ex:
p(1 or 6) in dice toss
= 1/6 +1/6
p(H or T) in coin flip
1/2 + 1/2
if not mutually exclusive events
p(a) + p(b) - P(a and b) = p(a) + P(b) - p(a and b)
p(king or heart)
(4/52 + 13/52) - (4/52)*(13/52)
multiplication rule
if 2 events are independent the probability of them occurring together is the product of their separate probabilities
p(a) * p(b)
ex:
flip 2 coins what is probability they both come up heads
p(head, head)
1/2 * 1/2 = .25
if events are not independent don’t do a sample replacement
joint
the probability of co occurrence of 2 or more events p(a,b)
conditional probability
the probability that one event will occur given that some event has occurred
denoted p(a/b)
the probability of a given b
the probability of A, if b is true
