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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
