Question 752434: 60% of all families in an eastern U.S. city subscribe to “The Atlantic Journal”, 45% subscribe to “The Daily News” and 20% subscribe to both “The Atlantic Journal” and “The Daily News”.
a) A family is selected at random from this city. What is the probability that this family subscribes to “The Atlantic Journal” or “The Daily News”?
b) A family is selected at random from this city. If this family subscribes to “The Daily News”, what is the probability that it does not subscribe to “The Atlantic Journal”?
c) A family is selected at random from this city. What is the probability that this family does not subscribe to either newspaper?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 60% of all families in an eastern U.S. city subscribe to “The Atlantic Journal”, 45% subscribe to “The Daily News” and 20% subscribe to both “The Atlantic Journal” and “The Daily News”.
let A represent the people who subscribe to the Atlantic Journal.
let B represent the people who subscribe to the Daily News.
a) A family is selected at random from this city. What is the probability that this family subscribes to “The Atlantic Journal” or “The Daily News”?
60% of all the people subscribe to A.
45% of all the people subscribe to B.
20% of all the people subscribe to both A and B.
that leave 40% of the people who subscribe to A only.
that leaves 25% of the people who subscribe to B only.
you still have 20% of the people who subscribe to both A and B.
add these up and you have 85% of the people who subscribe to A or B.
40% A only + 25% B only + 20% both A and B gives you a total of 85%.
the official formula for this is p(A and B) = p(A) + p(B) - p(A and B).
.6 + .45 - .2 = .85
b) A family is selected at random from this city. If this family subscribes to “The Daily News”, what is the probability that it does not subscribe to “The Atlantic Journal”?
60% of the people subscribe to A.
this includes 20% of the people who subscribe to both A and B.
this leaves 40% who subscribe only to A.
the percent of the people who subscribe to A but do not subscribe to B equals 40/60 = 66 and 2/3 percent.
the official formula for this is tricky, but it works.
the formula is:
p(not B given A) = p(not B and A) / p(A).
p(not B and A) is equal to p(A only) which is equal to p(A) - p(A and B).
that equals .6 - .2 = .4
p(not B given A) = p(not B and A) / p(A) = .4 / .6 = .66+2/3 = 66 and 2/3 percent.
c) A family is selected at random from this city. What is the probability that this family does not subscribe to either newspaper?
the probability is 15%.
the universe contains people who are in A or B or not in (A or B).
since 85% are in A or B, this leave 15% that are not in (A or B).
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