conditioner probability

Question 1

bayes theorem

Answer 1

• P(AnB) = P(A)P(B|A) = P(B)P(A|B)

Question 2

another way to write P(AnB)

Answer 2

P(A, B) “joint distribution” (used only by clowns)

Question 3

what do AuB and AnB mean

Answer 3

union (logical or) and intersection (logical and)

Question 4

how to calculate P(AnB)

Answer 4

P(A)P(B|A) or vice versa

Question 5

how to calculate P(AuB)

Answer 5

P(A) + P(B) - P(AnB)
(remember the venn diagram)

Question 6

P(AnB) when A and B are independent

Answer 6

• P(AnB) = P(A)P(B|A)
• independent -> P(B|A) = P(B)
• so P(AnB) = P(A)P(B)