Consider the Venn diagram below. The numbers in the regions of the circle indicate the number of items that belong to that region.

Question

(2 intersecting circles A & B, where A part is 50, B part is 110, and the intersecting part is 40)

Determine:

n(A)
n(B)
P(A)
P(B)
P(A|B)
P(B|A)

Answer 1

counting all the numbers in A I see n(A) = 90
n(B)=150
total is 200 , P(A) = 90/200 = 9/20

P(B) = 150/200 = 3/4

P(A|B) is a conditional probability and is defined as
P(A∩B/P(B)
= (40/200) / (3/4) = 4/15

find P(B|A) the same way

Answer 2

missed a bracket ...

P(A|B) is a conditional probability and is defined as
P(A∩B) / P(B)