Department

Statistics

Course Code

STAT1008

Professor

Bronwyn

Study Guide

Final

Probability

11.1 Probability Rules

• Event – soethig that either happes or does’t happe is true or is ot true.

• Probability of event (A) is the long-run frequency or proportion of times the event occurs.

• Probability always between O and 1.

• P(A) = 1 means A will definitively happen.

• P(A) = 0 means A will definitively not happen.

• If there are equally likely outcomes, then P(A) = no. of outcomes of event A/total no. of

outcomes.

Combination of Events

• P (A and B), or P (A or B).

Additive Rule

• P (A or B) = P(A) + P(B) – P(A&B).

• Use Venn diagram.

Complement Rule

• P (not A) = 1 – P(A).

• P (not (A or B)) = 1 – [P(A) + P(B) – P(A and B)]

Conditional Probability

• P (A if B) = P(A and B)/P(B), is the probability of A, if we know B

has happened.

• You may also see this written as P (A I B).

• This is read i ultiple ays: proaility of A if B, proaility

of A gie B or proaility of A oditioal o B.

• Note: P (A if B) ≠ PB if A.

Multiplicative Rule

• P (A and B) = P (A if B) P (B).

• Equivalent form: P (A and B) = P (A) P (B if A).

Special Case: Disjoint

Events

• Events A and B are disjoint or mutually exclusive if only one of

the two events can happen.

• If A and B are disjoint, then P (A or B) = P (A) + P(B).

• If A and B are disjoint, then both cannot happen, so P(A and B) =

0.

Special Case:

Independent Events

• Events A and B are independent if P (A if B) = P (A).

• Intuitively, knowing that event B happened does not change the

probability that event A happened.

• If A and B are independent, then P (A and B) = P(A)P(B).

11.2 Tree Diagrams and Bayes' Rule

Total Probability Rule

• For any two events A and B, P(B) = P(A and B) + P(not A and B) = P(A)P(B if A) + P(not A)P(B if

not A).

• If events B1, B2, through Bn are disjoint and together make up all possibilities, then: P(A) = P(A

and B1) + P(A and B2 + … + PA ad Bn).

Tree Diagrams

• The initial set of branches show the probabilities from one set of events and the second set of

branches show conditional probabilities.

• Multiplying along any set of branches uses the multiplicative rule to find the joint probability

for that pair of events.

Bayes' Rule

If A and B are any two events:

• P(A if B) = P(A and B)/P(B)

• Bayes’ Rule arious fors:

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