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In a certain residential suburb,, 60% of all households subscribe to the metropo

ID: 2922407 • Letter: I

Question

In a certain residential suburb,, 60% of all households subscribe to the metropolitan newspaper published in a nearby city, 80% subscribe to the local afternoon paper, and 50% subscribe to both papers. The events A and B are described as follows:

A = a household subscribes to the metropolitan paper

B = a household subscribes to the local paper

a. What is the probability that a household subscribes to the local newspaper, given that it subscribes to the metropolitan paper

b. If a ho usehold is selected at random, what is the probability that it subscribes to EXACTLY one of the two newspapers?

Explanation / Answer

A: households subscribe to the metropolitan newspaper

B: subscribe to the local afternoon paper

p(A)=0.6 and p(B)=0.8

p( A and B)=0.5

a) p(B|A)=p(A and B)/p(A)=0.5/0.6 =0.833

b) p(exactly one of the newspapers)=p(A)+p(B)-2*p(A and B)

we need to remove two times p(A and B) because we dont want anything in the common region of the venn diagram

Thus p(exactly one of the newspapers)=0.6+0.8-2*0.5= 0.4