Sample space: Set of all possible outcomes

Event: Outcome or set of outcomes. A subset of the sample space

Probability=Count of outcome/Count in sample space

Mutually exclusive? Can they happen at the same time? If yes,

then evaluate independence. If no, always dependent. Can use

addition rule

â€¢

Independent? Does knowing one occurs change the likelihood of

the other occurring? If yes, then dependent and use conditional

probabilities. If no, then independent and can use multiplication

rule.

â€¢

Mutually Exclusive/Disjoint events:

1)

they have no outcomes in common and can never occur

together

â€¢

ALWAYS dependent

â€¢

Think non overlapping Venn diagram

â€¢

Addition Rule:

P(D OR S)=P(D) + P(S)-P(D AND S)

â€¢

For any event A, P(A does not occur)=1-P(A)

â€¢

Non disjoint/ NOT mutually exclusive:

2)

Think Venn Diagram

â€¢

Both events can occur at the same time

â€¢

When A and B ARE independent variables

A)

Multiplication Rule= P(A and B)=P(A) x P(B)

To determine if something happens multiple times in a row a

certain number of times, P(E1, E2, E3 and E4)=P(E1)x P(E2)x

P(E3) x P(E4)

â€¢

Conditional Probability:

B)

When A and B are NOT independent

â€¢

Probabilities

October 9, 2015

5:24 PM

Probabilities Page 1

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