{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

IndependenceConditioning

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

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Learning Objectives Define conditional probability Calculate conditional probabilities for discrete events (e.g., coin tosses). Define independence
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example 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?
Background image of page 2
Conditional Probability Reason based on partial information Conditional probability of A given B P ( A | B )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example Roll a fair six-sided di P( outcome is 6 ) = 1/6
Background image of page 4
Example Roll a fair six-sided di What is P(outcomeis 6| outcomeis even)? P( | ) = outcome is even outcome is 6 1/3
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 6
Example Roll two fair 6-sided dice A = both show the same number P( A ) = 6 / 36
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example Roll two fair 6-sided dice B = their sum is not greater than 3 P( B ) = 3 / 36
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}