QTM 100 CH 3

probability

proportion of times the outcome would occur if we observed the random process an infinite number of times

Law of Large Numbers

the tendency of proportion of outcomes to stabilize around calculated probability (empirical => classical)

think experiments

how to write probability of xx happening

p(xx)

disjoint

two outcomes cannot occur at the same time

another term for disjoint is

mutually exclusive

how do you calculate disjoint probability

add up probabilities of each thing occuring

what word is associated with disjoint outcome

or

addition rule

P(A1 or A2)= P(A1)+P(A2)-P(A1andA2)

events

sets/collections of outcomes

ex: group a: if you roll 1 or 2, group b: if you roll 2 or 3

nondisjoint outcomes

when outcomes can overlap

ex: roll 2 and even

face card

jack, queen, king

how many cards in a deck of cards

52

Or is

inclusive (so it is and/or)

Why would (P and B) be 0 if outcome is disjoint

because they would never overlap

probability distribution

table of all disjoint outcomes and their probabiliteis

rules for probability distributions*

1. outcomes listed must be disjoint

2. each probability must be between 0 and 1

3. probabilities must total 1

sample space

all possible outcomes

complement of x

all outcomes that are not x

P(x or x1)= 1

independent

when outcome of one provides no useful info about another outcome (like flipping a coin and rolling a dice)

when do you use multiplication rule vs addition rule

multiplication: independent

addition: disjoint

multipplication rule

P (A and B) = P(A) x P (B)

who is the father of probability

Jerome Cardan

classical probability

#ways e can occur / total possible outcomes

empirical probability

#ways E occured/total # attempts

limitation of probability

cannot PROVE anything with probability

can disjoint outcome also be independent?

no because disjoint occurs at differnet times and independent is at same time

@ least 1 means

1 OR MORE

complement of at least 1 is

0 cuz otherwise you have no options

Contingency table includes

cases are horizontal and results are vertical

marginal probabilities

probability based on single variable

joint probability

probability of outcomes for two ore more variables

table proportions

data presented shows a proportional relationship between two variables

conditional proabability

compute probability under a condition

two parts of conditional probability

outcome of interest and condition

how to read out P( X| Y)

probability of x given y

conditional probability formula

P(A|B)= P(A and B)/P(B)

general multiplication rule

P(A and B)= P(A|B) x P (B)

gamblers fallacy

casinos post last several outcomes of betting games to trick gamblers into believing odds are in their favor

ex: all black last time, you believe it is unlikely you will get black

tree diagram

organize outcome and proability around structure of data

primary v secondary branch

primary: first branch (split)

secondary: other splits

false negative and false positive

shows up as positive/negative (true/untrue) even when it isn’t

without replacement

you cannot sample the same case twice

what do you have to do with a “without replacement” situation

remove from possibilities

when should you use at least rule

when you need to calculate the likelihood of an event happening at least once in a given set of trials

when sample size is nearly less than 10% of pop, observations are

independent

If P(A and B) = P(A) P(B), A and B are

independent

If P(B) = P(B |A), then A and B are

independent

Binomial distribution

Describes number of success in fixed number trials (usually one or the other)

Difference between binomial and geometric distribution

Geometric: describe number of trails you must wait before success

Binomial: number of success in fixed number trials

Binomial distribution formula

(N!/K!(n-k)!)*p^k(1-p)^n-k

What do variables in formula mean?

N= number of trials

K= number successes

Mean, variance, and SD formula of observed successes

Mean: np

SD²=np(1-p)

Four conditions to check if binomial

1. Independent trials

2. Number of trials n is fixed

3. Each trial can be classified as success or failure

4. Probability of success p is the same for each trial

How to solve binomial distribution with normal distribution steps

ONLY TO BE USED WITH LARGE SAMPLES!!!

Treat all steps normal except add 0.5

Continuity correction value

.5

Most vs more

Most= include

More= does not include