Q:

Is this Event Mutally Exclusive? 

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) = ? 

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
$$A \cup B = \{2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19, 20\}.$$

