Unit4) Probability

Mutually Exclusive

Two events have NO overlap & cannot occur at the same time

Independent

Two events with probabilities that DO NOT effect one another

• EX.) Rolling a die and flipping a coin

P(A or B)

IF NOT MUTUALLY EXCLUSIVE…

• Add P(A) and P(B), then subtract their overlap P(A) + P(B) - P(A and B) 

IF MUTUALLY EXCLUSIVE

• Add P(A) and P(B) 

P(A and B) ; at the SAME TIME 

IF NOT INDEPENDENT

• Multiply P(A) with the P(A |B) ==> P(A) * P(A | B) 

IF INDEPENDENT

• Multiply P(A) and P(B) 

Complement

The probability in which an event does NOT occur

P(A^C) = 1 - P(A)

Sample Space

All the possible combinations in a simulation when looking for probability

Simulation

A model used to mimic real-world events to estimate probabilities

FOUR MAIN STEPS…

1) DEFINE the problem/question

2) DESCRIBE how to model the situation correctly

3) PERFORM multiple trials

4) CONCLUDE using results to estimate probability

Probability

The CHANCE that an event will happen in the long term

• Written as a decimal between (and including) 0 and 1

• UNPREDICTABLE short term

• PREDICTABLE in the long term

• Many random trials have to be observed to start approaching actual probability value 

PROBABILITY IS EMPIRICAL !!