A survey was made about two daily newspapers, LOS ANGELES TIMES and THE NEW YORK TIMES, 105 people bought Los Angeles Times, 25 did not buy Los Angeles Times, 95 did not buy New York Times, while 83 bought Los Angeles times but not New York Times.
How many people took part in the survey?
assuming there were no people in the survey population who did not respond to all questions, the population size would be
LAT + not-LAT = 105 + 25 = 130
because the two subsets are mutually exclusive, i.e., the intersection of those two subsets is empty
thus all members of the population must be contained in one or the other of those two subsets
the sum of those two sets is the total population
To find out how many people took part in the survey, we can use a basic principle of set theory called the Inclusion-Exclusion principle.
Let's break down the information provided:
1. We know that 105 people bought the Los Angeles Times.
2. We know that 25 people did not buy the Los Angeles Times.
3. We know that 95 people did not buy the New York Times.
4. We know that 83 people bought the Los Angeles Times but did not buy the New York Times.
Let's use this information to calculate the total number of people who took part in the survey.
First, we can find the number of people who bought both newspapers. Since we know that 83 people bought the Los Angeles Times but not the New York Times, we subtract this number from the total number of people who bought the Los Angeles Times:
105 - 83 = 22 people bought both newspapers.
Next, we need to find the number of people who only bought the New York Times. We can do this by subtracting the number of people who bought both newspapers from the total number of people who did not buy the New York Times:
95 - 22 = 73 people only bought the New York Times.
Now, we can calculate the total number of people who took part in the survey:
Number of people who bought the Los Angeles Times + Number of people who did not buy the Los Angeles Times + Number of people who only bought the New York Times = Total number of people in the survey
105 + 25 + 73 = 203 people
Therefore, the total number of people who took part in the survey is 203.