04: Conditional Probability and Bayes

04: Conditional Probability and Bayes

Lisa Yan April 13, 2020

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Quick slide reference

3 Conditional Probability + Chain Rule 15 Law of Total Probability 22 Bayes' Theorem I 31 Bayes' Theorem II 61 Monty Hall Problem

Lisa Yan, CS109, 2020

04a_conditional 04b_total_prob

04c_bayes_i LIVE LIVE

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Conditional Probability

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Dice, our misunderstood friends

Roll two 6-sided dice, yielding values 1 and 2.

Let be event: 1 + 2 = 4. Let be event: 1 = 2.

What is ?

What is , given already observed ?

= 36 = 1,3 , 2, 2 , 3,1

= 3/36 = 1/12

Lisa Yan, CS109, 2020

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Conditional Probability

The conditional probability of given is the probability that occurs given that F has already occurred. This is known as conditioning on F.

Written as: Means: Sample space Event

(|) " , given already observed " all possible outcomes consistent with (i.e. ) all outcomes in consistent with (i.e. )

Lisa Yan, CS109, 2020

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