Chapter 1

Question 1

P(A U B) = ?

Answer 1

P(A) + P(B) - P(A ∩ B)

Question 2

P(A U B U C) = ?

Answer 2

P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Question 3

Morgan’s law

Answer 3

P((A U B)’) = P(A’ ∩ B’)
P((A ∩ B)’) = P(A’ U B’)

Question 4

P(A|B) = ?

Answer 4

P(A ∩ B)/P(B)

Question 5

Independence

Answer 5

P(A ∩ B) = P(A) x P(B)
P(A|B) = P(A)
P(B|A) = P(B)

Question 6

Bayes theorem

Answer 6

Pr(A|B) = Pr(B|A_k) x P(A_k) / Somme de Pr(B|A_i) x P(A_i)