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STAT 430/510 Lecture 5 STAT 430/510 Probability Hui Nie Lecture 5 June 2nd, 2009

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STAT 430/510 Lecture 5 Review Sample Spaces and Events Axioms and Properties of Probability Sample Spaces Having Equally Likely Outcomes
STAT 430/510 Lecture 5 Conditional Probability The Probability of an event measures how often it will occur. A conditional probability predicts how often an event will occur under specified conditions. Notation: P ( E | F ) represents the conditional probability that event E occurs, given that event F has occurred.

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STAT 430/510 Lecture 5 Definition Definition If P ( F ) > 0, then P ( E | F ) = P ( EF ) P ( F ) The "condition" F contains partial knowledge.
STAT 430/510 Lecture 5 Example A coin is flipped twice. Assuming that all four points in the sample space S = { ( H , H ) , ( H , T ) , ( T , H ) , ( T , T ) } are equally likely, what is the conditional probability that both flips land on heads, given that (a) the first flip lands on heads? (b) at least one flip lands on heads?

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STAT 430/510 Lecture 5 Example A stock market analyst feels that
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