Ch. 3 Conditional probability and independence

Question 1

P(A | B) =

Answer 1

P(A | B) = P(A n B) / P(B)

Question 2

P(A n B | C) =

Answer 2

P(A n B | C) = P(B | C)P(A | B n C)

Question 3

Bayes’ theorem, for events A, B and C
P(A | B) =
P(A | B n C) =

Answer 3

P(A | B) = P(A)P(B | A) / P(B)

P(A | B n C) = P(A | C)(P(B | An C) / P(B | C)

Question 4

Definition of independence of 2 events A and B

Answer 4

P(A n B) = P(A)P(B)

Question 5

2 events A and B are conditionally independent if given a third event C:

Answer 5

P(A n B | C) = P(A | C)P(B | C)