A large cable company reports that 70% of its customers subscribe to its cable TV service, 34% subscribe
to its Internet service, and 93% subscribe to at least one of these two services.
(a) Use the given probability information to set up a hypothetical 1,000 table.
Cable TV Not Cable TV Total
Internet Service ______ _______ _____
Not Internet Service ______ _______ _____
Total ______ _______ 1000
(b) Use the table from part (a) to find the following probabilities.
(i) the probability that a randomly selected customer subscribes to both cable TV and Internet
service
(ii) the probability that a randomly selected customer subscribes to exactly one of these services
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b) 0.2944
c) 0.1111
d) 0.065
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(a) Using the given probability information, we can set up the table as follows:
Cable TV Not Cable TV Total
Internet Service 63 x 734
Not Internet Service 10 x 207
Total 70 930 1000
We can find the values for "Not Cable TV" and "Not Internet Service" by subtracting the given probabilities (70% and 34% respectively) from 100%.
(b)
(i) The probability that a randomly selected customer subscribes to both cable TV and Internet service is 63/1000 or 0.063.
(ii) The probability that a randomly selected customer subscribes to exactly one of these services can be calculated by adding the probabilities for "Cable TV only" and "Internet Service only".
The probability for "Cable TV only" is (70 - 63)/1000 or 0.007, since 70% subscribe to Cable TV and 63/1000 subscribe to both.
The probability for "Internet Service only" is (34 - 63)/1000 or 0.034, since 34% subscribe to Internet Service and 63/1000 subscribe to both.
Therefore, the probability that a randomly selected customer subscribes to exactly one of these services is 0.007 + 0.034 or 0.041.
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