Stats Ch. 9 - Essential Probability

Chance Behavior

Unpredictable in short term but predictable over time
ex) flipping a coin 4 times doesn’t mean that it will be heads exactly twice and tails twice, but do it 100 times and it will most likely be heads half the time and tails half the time.

Probability Model

Includes Sample Space (S) and probability assignments (P)

Sample Space (S)

The set of all possible outcomes

the letter P

P assigns a probability
ex) P(A), what is the probability that P(A) will happen?

Personal Probabilities

A person’s personal self judgement on how many times something will happen

Basic Properties of Probability

For any event, the probability P(A) must be between 0 to 1, P(S) is 1
For P(A & B) = 0 then they have no outcomes in common and cannot happen at the same time
then this means P(A or B) = P(A) + P(B)
For P(A doesn't happen) = 1 - P(A)

Discrete Probability Model

Sample Space S has a finite number of values. Each value will get a number from 0-1 and they will add up to 1 in total0