Probability - stats

Probability theory

Branch of maths describes random behavior

Basis of probability

Observation

Probability

Extent to which an event, consist of single outcome is likely to occur and represent as proportion

Probability of event, P(E)

Numbers between 0-1 indicate likelihood that it occur

Spread of probability

0≤P(E)≤1 for any event E

If event certain not to occur

Probability is 0

If event is certain to occur

Probability is 1

Theoretical probability

Expected probability, equal

Law of large numbers

As sample size increase, expect experimental probability to be closer to theoretical probability value of those outcomes

Write probability in

Fraction or decimal

3 methods of expressing probability

Institution, Experimental and theoretical

Intuition

Guessing the probability

Experimental probability

After calculating

Outcomes

In any probability, different possible results

Sample space

List in brackets of all possible outcomes in any probability experiment.

All P(E) added equals to

1

Ven diagram

Probability spaces and events can be illustrated with Venn diagram

P(E)≤P(S)

Probability of any event is subset of sample space

Complement

Probability of event not happening

Tree diagram

Helps display outcome of probability experiment consisting of series of outcomes. Total number of outcomes corresponds to total number of final branches.

Chance experiment

Activity where 1 situation in which there is uncertanity

All data collected for

chance experiment

event

any collection of outcomes from sample space of chance

Union

Event A or B consists of all experimental outcomes that are in at least 1 of 2 events

Intersection

Event A and B consist of all experimental outcomes

Disjoint

2 events that have no common outcomes

Probability distribution

List of all outcomes in sample space and their probabilities

If A and B are independent events, P(A &B)

Multiply probabilities

Conditional probability

Knowledge of 1 event occurring changes other events

Conditional prob written as

Prob of A occuring given that B has already occured

Union, or, calculate

Add individual and then subtract common

Permutation

arrangement of objects where order matters

Combination

arrangement of objects where order doesn’t matter