Conditional Probability

Question 1

Conditional probability

Answer 1

Let A and B be the two events:
–> P(B) > 0

The conditional probability of A given B is defined by

P(A|B) = P(A∩B) / P(B)

Question 2

Remarks of conditional probability

Answer 2

–> The roles of A and B are different:
A: conditioned event
B: conditioning event

–> In general
P(A|B) != P(B|A)

–> P(A°|B) = 1 - P(A|B)

–> P(A1 U A2|B) =
P(A1|B) + P(A2|B)

Question 3

Properties of conditional probability

Answer 3

1) P(A∩B) = P(A|B)*P(B)

2) P(A)=P(A∩B) + P(A∩B°)
P(A)= (P(A|B)P(B)) +
(P(A|B°)P(B°))

Total probability
P(A) = Σ P(A|Bk) * P(Bk)

3) Bayes Formula
P(B|A)=
( P(A|B)*P(B) ) / P(A)