SOLUTION: 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 N

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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