Question

Given: P(A) = 0.45, P(B) = 0.65, and P(A and B) = 0.35.

Find:

P (A or B)

P(A OR B) ( line on top)

P(A|B)

P(B|A)

Answer 1

• P(A or B) = 0.75
• P(A or B)' = 0.25
• P(A|B) = 0.54
• P(B|A) = 0.78

Explanation:

Normally we use the symbols U for set union corresponding to or and ∩ for set intersection corresponding to and.

But here i will use and and or

By the rules of probability

P(A or B) = P(A) + P(B) - P( A and B)
So P(A or b ) = 0.45 + 0.65 - 0.35 = 0.75

The complement of a set A is all the elements not in A
P(A') = 1 - P(A)

If we denote the complement of a set A as A' then your second expression is asking What is the complement of A or B or P(A or B)'
P(A and B)' = 1 - P(A or B) = 1- 0.75 = 0.25

P(A|B) = P(A and B)/P(B) = 0.35/0.65 = 0.54

P(B|A) = P(A and B)/P(A) = 0.35/0.45 = 0.78