I am trying to calculate the following, however I'm unsure on whether this event would be Mutally Exclusive or Independent.
Can someone help with finding the probability of the Intersection?
P(A) = 7/20
P(B) = 1/2
P(A Intersection B) = ? ^ Would this simply be (7/20) * (1/2) ?
P(A Union B) = ?
P(B | A) = ?
If you actually write out the sets A and B, you can easily compute the intersection.
$$\Omega = \{1..20\}$$ $$A = \{14, 15, 16, 17, 18, 19, 20\}$$ $$B = \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}$$ With this you get $$A \cap B = \{14, 16, 18, 20\}$$ by simply looking at which elements are in both sets. Thus $$ P(A \cap B) = \frac{|A \cap B|}{|\Omega|} = \frac{4}{20} $$ which is not the same as $$P(A)*P(B) = \frac{7}{20} * \frac{1}{2} = \frac{3.5}{20},$$ because A and B are not independent.
Likewise for the union you get $$A \cup B = \{2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19, 20\}.$$