4.4 The Multiplication Rule for "And" Probabilities Theory

What is the Multiplication Rule?

(1) the probability of “A” occurring and then “B” occurring in successive trials

(2) happens in two trials

What is the difference between the addition rule and the multiplication rule?

(1) P(A and B) in the addition rule formula mean both occur during a single trial

(2) P(A and B) in the multiplication rule mean probability A occurring and then probability B occurring in two trials

Multiplication Rule Formula

(1) For Independent Events, With Replacement

• P(A and [then] B) = P(A) ⋅ P(B)

(2) For Dependent Events, Without Replacement

• P(A and [then] B) = P(A) ⋅ P(B|A)

What is conditional probability?

(1) a probability that is dependent on a previous event

(2) the probability of some event occurring, given that another event has already occurred

Notation of Conditional Probability

P(B|A)

P(B|A) is read in plain English as…

“the probability of B given that A has already occurred”

What is an independent event?

(1) stand alone events

(2) an occurrence of one event does not affect the occurrence of another event

Given that P(B|A), if event B is independent, what does P(B|A) equal to?

P(B|A) = P(B)

What does with replacement mean?

(1) you keep the same number of simple events when you use the multiplication rule (recall no. of events / simple events)

(2) independent events make up with replacement

What does without replacement mean?

(1) the number of simple events goes down when you use the multiplication rule (recall no. of events / simple events)

(2) dependent events make up without replacement