Answer Key
Suppose A and B are two events with probabilities:
P(Ac )=.40,P(B)=.45,P(A∪B)=.60.
Find the following:
a) P(A∩B).
For P(A∩B). Use P(A∪B)=P(A)+P(B)-P(A∩B) and rearrange to
P(A∩B)=P(A)+P(B)-P(A∪B). But for this equation, we need P(A) which we can find by using P(A)=1-
P(A^c ). So, P(A)=1-.40= .60.
P(A∩B)=.60+.45-.60=.45.
b) P(A).
P(A) was found above as .60.
c) P(Bc).
For P(Bc ). Use P(B)=1-P(Bc ) which may be rearranged to (Bc )=1-P(B).
P(Bc )=1-.45=.55.
Exam Page 2
Suppose you are going to make a password that consists of 4 characters chosen from
{2,7,8,c,f,k,t,z}. How many different passwords can you make if you cannot use any character more
than once in each password?
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