Conditional Probability and Independence

Conditional Probability and Independence

Christopher Croke

University of Pennsylvania

Math 115

Christopher Croke

Calculus 115

Probability

The probability of an event depends on the sample space.

Christopher Croke

Calculus 115

Probability

The probability of an event depends on the sample space. Problem: In a group of 30 athletes 12 are women, 18 are swimmers, and 10 are neither. A person is chosen at random.

Christopher Croke

Calculus 115

Probability

The probability of an event depends on the sample space. Problem: In a group of 30 athletes 12 are women, 18 are swimmers, and 10 are neither. A person is chosen at random. What is the probability that it is a female swimmer?

Christopher Croke

Calculus 115

Probability

The probability of an event depends on the sample space. Problem: In a group of 30 athletes 12 are women, 18 are swimmers, and 10 are neither. A person is chosen at random. What is the probability that it is a female swimmer? Here we find (from inclusion/exclusion) that #(S W ) = 10 so

#(S W ) 10 1

Pr (S W ) =

= =.

total# 30 3

Christopher Croke

Calculus 115

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