Biostats Unit 3 Probability

outcome

a potential result of a random process

sample space

the set of all outcomes

event

a set of outcomes (a subset of the sample space)

probability

an assignment of numbers to events to indicate how likely they are to occur

Never = 0 = 0% chance to happen

Always = 1 = 100% chance to happen

empirical method for computing probability

Simulate the random process

number of time event happens divided by the number of times we repeated the random process

theoretical method uses

probability rules!

P(S) = 1 what is this?

total probability

S is the sample space

mutually exclusive

The events cannot both happen at the SAME time

If one happens, the other cannot

General Addition Rule

P(A or B) = P(A) + P(B) - P(A and B)

Additivity rule for mutually exclusive events

P(A or B) = P(A) + P(B)

Equally likely rule

P(A) = number of outcomes in A divided by number of outcomes in sample space

each outcome has a probability of 1/N where N is the total size of the sample space

complement rule

The probability of something NOT happening is 1 minus the probability it DOES occur

multiplication rule

determines the likelihood of two or more events occurring together by multiplying probabilities

equation changes based on whether the event is independent or dependent

Multiplication rule for independent events

P(A and B) = P(A) * P(B)

Multiplication rule for dependent events

P(A and B) = P(A) P(B|A) or P(B) * P(A|B)

P(A if B)

P(A|B)

conditional probability equation

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

independent events

two events are independent if the outcome of one does NOT affect the probability of the other

dependent events

the outcome of one event affects the probability of the other