A survey asks people about their reading habits with respect to three newspapers. The results
show that 56% read newspaper A, 33% read newspaper B, and 27% read newspapers C. 7% of the
respondents read newspapers A and B, 8% of the respondents read newspapers B and C, 11% of
the respondents read newspapers A and C, 2% of the respondents read newspapers A, B, and C.
What is the percentage of people reading none of the newspapers?
perfect case for a Venn diagram solution
draw 3 intersecting circles, and fill in the data
add up all the entries,
100 - (above sum) is the number who don't read any of the three
To find the percentage of people reading none of the newspapers, we need to subtract the percentage of people reading at least one newspaper from 100%.
Let's break down the information given:
- 56% read newspaper A
- 33% read newspaper B
- 27% read newspaper C
- 7% read newspapers A and B
- 8% read newspapers B and C
- 11% read newspapers A and C
- 2% read newspapers A, B, and C
To find the percentage of people reading at least one newspaper, we need to add up the percentages of people reading each newspaper individually and subtract the percentages of people reading multiple newspapers (to avoid double counting).
Percentage of people reading at least one newspaper = (Percentage of people reading newspaper A) + (Percentage of people reading newspaper B) + (Percentage of people reading newspaper C) - (Percentage of people reading newspapers A and B) - (Percentage of people reading newspapers B and C) - (Percentage of people reading newspapers A and C) + (Percentage of people reading newspapers A, B, and C)
= 56% + 33% + 27% - 7% - 8% - 11% + 2%
= 92%
Now, to find the percentage of people reading none of the newspapers, we subtract the percentage of people reading at least one newspaper from 100%:
Percentage of people reading none of the newspapers = 100% - Percentage of people reading at least one newspaper
= 100% - 92%
= 8%
Therefore, the percentage of people reading none of the newspapers is 8%.