week3 - Conditional Probability Idea have performed a...

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week 3 1 Conditional Probability Idea – have performed a chance experiment but don’t know the outcome ( ω ), but have some partial information (event A ) about ω . Question: given this partial information what’s the probability that the outcome is in some event B ? Example: Toss a coin 3 times. We are interested in event B that there are 2 or more heads. The sample space has 8 equally likely outcomes. The probability of the event B is … Suppose we know that the first coin came up H. Let A be the event the first outcome is H. Then and The conditional probability of B given A is {} TTT TTH THT HTT THH HTH HHT HHH , , , , , , , = Ω ( ) () A P B A P = = 8 4 8 3 4 3 { } HTT HTH HHT HHH A , , , = { } HTH HHT HHH B A , , =
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week 3 2 Given a probability space ( , F , P ) and events A, B F with P( A ) > 0 The conditional probability of B given the information that A has occurred is Example : We toss a die. What is the probability of observing the number 6 given that the outcome is even? Does this give rise to a valid probability measure?
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week3 - Conditional Probability Idea have performed a...

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