Conditional probability

Question 1

Define independent events, and give relevant equations

Answer 1

Two events are independent if the outcome of one event doesn’t affect the other

P(A|B) = P(A) or P (B|A) = P(B)

Also P(A∩B) = P(A) . P(B)

Question 2

Define mutually exclusive events, and give relevant equations

Answer 2

Two events that can’t occur at the same time

P(A∩B) = 0

Question 3

What is the multiplication rule for conditional probability?

Answer 3

P(A|B) = P(A∩B) / P(B)
or
P(A∩B) = P(A|B) . P(B)

Question 4

Events A and B are such that
P(A ∩ B’) = 0.24, P(B) = 0.35 and P(A|B) = 0.1

Work out P(A ∪ B)

Answer 4

P(A∩B) = P(A|B) . P(B)
= 0.1 . 0.35
= 0.035

P(A∪B) = P(A) + P(B) - P(A∩B)
P(A) = P(A∩B') + P(A∩B) = 0.24 + 0.035 = 0.275

P(A∪B) = 0.275 + 0.35 - 0.035

=0.59