Final Review – Probability Definition of Probability Sample Space is = set of all possible outcomes. Event Space is = set of all outcome of type E. Probability of event is ( ) . Overview of Probability is a subset of . So always have . Always have ( ) . ( ) means event NEVER happens. ( ) means event ALWAYS happens. For 0 < P(E) < 1 , P(E) measures how likely the event is to happen. Closer to 1 = more likely.
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Final Review – Probability
Definition of Probability
Sample Space is = set of all possible outcomes.
Event Space is = set of all outcome of type E.
Probability of event is ( )
.
Overview of Probability
is a subset of . So always have .
Always have ( ) .
( ) means event NEVER happens.
( ) means event ALWAYS happens.
For 0 < P(E) < 1 , P(E) measures how likely the
event is to happen. Closer to 1 = more likely.
Final Review – Probability
Rules of Probability
Let be the sample space.
Rule 1 : ( ) ( ) ( ) .
Rule 2: P(not E) = 1 – P(E).
Rule 3: Events are MUTUALLY
EXCLUSIVE if they have no common outcome.
(e.g., = exactly 2 Heads, = exactly 3 Heads)
P( ) ( ) ( ).
Rule 4: Events are INDEPENDENT
if they do not affect each other.
(e.g., = first die is 3, = second die is 5)
P( ) ( ) ( )
Final Review – Probability
Odds and Probability
The odds in favor of an event are given as
F to U where F = Favorable, U = Unfavorable.
The odds against an event are U to F.
Formulas
Odds in Favor corresponding probability of success
F to U P =
Odds against correspond to probability of failure
U to F 1-P =
Probability of success corresponding Odds in Favor