IndependenceConditioning - Le arning Obje s ctive fine De...

Learning Objectives
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Define conditional probability
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Calculate conditional probabilities for discrete
events (e.g., coin tosses).
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Define independence

Example
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Suppose that two doctors test all patients coming into a blood
donation center for anemia. Suppose that the first doctor
diagnoses 10% of all patients as positive, the second doctor
diagnoses 17% of all the patients as positive, and both doctors
diagnose 8% of all patients as positive. What is the
conditional probability that the second doctor makes a
positive diagnosis of anemia given that the first doctor makes
a negative diagnosis?

Conditional Probability
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Reason based on partial information
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Conditional probability of A given B
P ( A | B )

Example
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Roll a fair six-sided di
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P( outcome is 6 ) = 1/6

Example
•
Roll a fair six-sided di
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What is P(outcomeis 6| outcomeis even)?
•
P( | ) =
outcome is even outcome is 6
1/3

Conditional Probability
•
Conditional probability of A given B
P ( A | B ) =
P ( A ∩ B )
P ( B )
P ( A | B ) =
P ( A ∩ B )
P ( B )
=
1
6
3
6
=
1
3

Example
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Roll two fair 6-sided dice
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A = both show the same number
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P( A ) = 6 / 36

Example
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Roll two fair 6-sided dice
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B = their sum is not greater than 3
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P( B ) = 3 / 36