Question

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

Determine
• n(A)
• n(B)
• P(A)
• P(B)
• P(A|B)
• P(B|A)

Answer 1

n(A)=90

Answer 2

n(B)=150

Answer 3

by counting

Answer 4

\[P(A)=\frac{90}{200}=\frac{9}{20}=.18\]assuming there is nothing outside the two circles

Answer 5

likewise
\[P(B)=\frac{150}{200}=\frac{3}{4}=.75\]

Answer 6

\[P(A|B)=\frac{40}{150}=\frac{4}{15}\]

Answer 7

because you know you are in B, and the question is "given you are in B, what is the probability you are also in A

Answer 8

and finally
\[P(B|A)=\frac{40}{90}=\frac{4}{9}\]

Answer 9

because you know you are in A (which has 90 elements) and the question is given you are in A what is the probability you are also in B