Portage Learning Math 110 Module 3 Exam
1.Find the answer to each of the following by first reducing the fractions
as much as possible:
a) P(412,3)=
b) C(587,585)=
2.Suppose you are going to make a password that consists of 5 characters chosen from
{1,2,4,9,d,i,k,m,n,w,z}. How many different passwords can you make if you cannot use
any character more than once in each password?
, 3.Suppose A and B are two events with probabilities:
P(A)=.35, P(Bc )=.45,
P(A∩B)=.25.
Find the following:
a) P(A𝖴B).
b) P(Ac ).
c) P(B).
a. For P(A𝖴B). Use P(A𝖴B)=P(A)+P(B)-P(A∩B) . But for this equation, we need
P(B) which we can find by using P(B)=1-P(Bc ). So, P(B)=1-.45= .55.
P(A𝖴B)=.35+.55-.25=.65
b. For P(Ac ). Use P(A)=1-P(Ac ) which may be rearranged to (Ac )=1-P(A) .
P(Ac )=1-.35=.65.
c. For P(B). Use (B)=1-P(Bc ) .
P(B)=1-.45=.55.
4.Suppose A and B are two events with
probabilities: P(Ac )=.50, P(B)=.65,
P(A∩B)=.30.
a) What is (A│B) ?
b) What is (B│A) ?
1.Find the answer to each of the following by first reducing the fractions
as much as possible:
a) P(412,3)=
b) C(587,585)=
2.Suppose you are going to make a password that consists of 5 characters chosen from
{1,2,4,9,d,i,k,m,n,w,z}. How many different passwords can you make if you cannot use
any character more than once in each password?
, 3.Suppose A and B are two events with probabilities:
P(A)=.35, P(Bc )=.45,
P(A∩B)=.25.
Find the following:
a) P(A𝖴B).
b) P(Ac ).
c) P(B).
a. For P(A𝖴B). Use P(A𝖴B)=P(A)+P(B)-P(A∩B) . But for this equation, we need
P(B) which we can find by using P(B)=1-P(Bc ). So, P(B)=1-.45= .55.
P(A𝖴B)=.35+.55-.25=.65
b. For P(Ac ). Use P(A)=1-P(Ac ) which may be rearranged to (Ac )=1-P(A) .
P(Ac )=1-.35=.65.
c. For P(B). Use (B)=1-P(Bc ) .
P(B)=1-.45=.55.
4.Suppose A and B are two events with
probabilities: P(Ac )=.50, P(B)=.65,
P(A∩B)=.30.
a) What is (A│B) ?
b) What is (B│A) ?
