A survey revealed that 44% of people are entertained by reading books, 46% are entertained by watching TV, and 10% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV?
Let total surveyed people be
We are given that
entertained by both TV and books.
(number of people entertained by EITHER books or TV)
The numbers that are given only tell us about the people who are entertained by books and TV only, but not about other forms of entertainment.
In the same way, the people who ONLY watch TV make up
Now we have the information that of people surveyed:
Only books =
Only TV =
Books and TV =
This makes up
There are therefore
The probability that a person is entertained by books or TV :
books or TV; and,
By what is given, we have,