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MATH 110 TEST 3- PORTAGE LEARNING
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MATH 110 TEST 3- PORTAGE LEARNING
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[DOCUMENT TITLE], Suppose A and B are two events with probabilities:
P(Ac )=.70,P(B)=.65,P(A∪B)=.80.
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(Ac ). So, P(A)=1-.70= .30.
P(A∩B)=.30+.65-.80=.15.
b) P(A).
P(A) was found above as .30.
c) P(Bc).
For P(Bc ). Use P(B)=1-P(Bc ) which may be rearranged to (Bc )=1-P(B) .
P(Bc )=1-.65=.35.
Suppose you are going to make a password that consists of 6 characters chosen from
{3,4,5,7,d,f,g,k,q,r,s,w}. How many different passwords can you make if you cannot use any
character more than once in each password?
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