Probability Basics

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Probability Basics
Probability for equally likely outcomes
The sum of the dice is 9.
Doubles are rolled.
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Probability Basics
Basic properties of Probabilities
1. The probability of an event is always between
0 and 1 inclusive.
2. The probability of an event that cannot occur
is 0.
3. The probability of an event that must occur is
1.
The probability that the sum of the dice is 1
The probability that the sum of the dice is 12 or
less
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Events
Sample Space The collection of all possible
outcomes for an experiment.
Event A collection of outcomes for the
experiment, that is, any subset of the sample
space.
Given a standard deck of cards find the
probability Event the card selected is the king
of hearts. Event the card selected is a
king. Event the card selected is a heart. Event
the card selected is a face card.
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Events
Venn Diagrams
Not E the event E does not occur.
A B the event A and B occur.
A or B The event either A or B occurs.
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Events
Given a standard deck of cards find the
probability Event the card selected is not a
face card. Event the card selected is a king and
a heart. Event the card selected is a king or a
heart. Event the card selected is a heart and a
face card.
Mutually exclusive events
Event the card selected is a 10 and a face card.
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Rules of Probability
Some rules of Probability
Probability Notation. P(E) If E is an event,
then P(E) is the probability that E occurs. Ie
The probability of E.
The Special Addition Rule If mutually exclusive
P(A or B) P(A) P(B)
The Complementation Rule P(E) 1 P(not E)
The General Addition Rule P(A or B) P(A)
P(B) P(A B)
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Rules of Probability
Given arrests in 1 year had the following
statistics 79.6 were male. 18.3 were under 18.
13.5 were males under 18.
Let M event person arrested is male.
Let E event person arrested is under 18.
Determine P(M or E)
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Contingency Tables
Contingency Tables 2 way tables.
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Conditional Probability
Conditional Probability
The probability that event B occurs given that
event A has occurred is called a conditional
probability. It is denoted P(B A) or the
probability of B given A.
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Conditional Probability
Rolling a die.
F event a 3 is rolled. O
event the die comes up odd
P(f), the probability that a 3 is rolled.
P(FO), the conditional probability that a 3 is
rolled given that the die comes up odd.
P(O(not F)), the conditional probability that
the die comes up odd given that a 3 is not
rolled..