6. Suppose that you’re given the following probabilities P(A) = 1/2 , P(B) = 1/4 , P(C) = 1/8 , P(A ∪ B) = 3/4 Find the following probabilities: • P(A ∪ B') • P(A' ∩ B')

Question

6. Suppose that you’re given the following probabilities

P(A) = 1/2 ,

P(B) = 1/4 ,

P(C) = 1/8 ,

P(A ∪ B) = 3/4

Find the following probabilities:

• P(A ∪ B')

• P(A' ∩ B')

Answer 1

P(A) = 1/2, P(B) = 1/4, P(C) = 1/8,

You can simply visualize this as a 3-circle Venn Diagram inside a Universal set U.

To illustrate with numbers, you can also pick number of elements as |U|=16, then probabilistically half of the elements will be in A |A|=8, |B|=4, |C|=2 and |Others|=2.

Since P(A ∪ B) = 3/4 = P(A)+P(B) = (1/2+1/4), this means sets A & B are NOT intersecting. P(A∩B)=0.

• P(A ∪ B') = P(B') since A is already outside B and its union with B' is a subset of B'. P(B')=1-1/4=3/4.

• P(A' ∩ B') = P(AUB)'= 1-3/4 = 1/4.