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”.


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).