In a survey of 500 people:55% use Instagram 45% use Reddit 35% use TikTok 25% use both Instagram and Reddit 15% use both Instagram and TikTok 10% use both Reddit and TikTok 5% use all three What percentage of people use at least one of the three apps?

Question

BlackTom AI · Accepted Answer

We start by listing the given percentages for each app and their overlaps to apply the inclusion-exclusion principle.
- 55% use Instagram (I)
- 45% use Reddit (R)
- 35% use TikTok (T)
- 25% use both Instagram and Reddit (I ∩ R)
- 15% use both Instagram and TikTok (I ∩ T)
- 10% use both Reddit and TikTok (R ∩ T)
- 5% use all three (I ∩ R ∩ T)

Next, apply the inclusion-exclusion formula for the union I ∪ R ∪ T:
P(I ∪ R ∪ T) = P(I) + P(R) + P(T) − P(I ∩ R) − P(I ∩ T) − P(R ∩ T) + P(I ∩ R ∩ T)
Plugging in the values: 55% + 45% + 35% − 25% − 15% − 10% + 5% = 135% − 50% + 5% = 90%
So, 90% of people use at least one of the three apps.

Now evaluate the answer choices:
- Option a: 80% — This undervalues the union; it would omit some people accounted for by the overlaps and singles, so it’s incorrect.
- Option b: 95% — This overstates the union; the inclusion-exclusion calculation yields 90%, so 95% is too high.
- Option c: 85% — Also too low; the computed total is 90%, so this option misses those counted in the singles minus overlaps plus the triple, making it incorrect.
- Option d: 90% — This matches the result from the inclusion-exclusion calculation, so it is correct.

In summary, by carefully adding the individuals using each app, subtracting the overlaps where people are counted multiple times, and then re-adding those who are counted in all three, the proportion who use at least one app comes out to 90%, which corresponds to option d.

FIT1058_S1_2025 Week 10 Pre-reading Quiz

In a survey of 500 people:55% use Instagram 45% use Reddit 35% use TikTok 25% use both Instagram and Reddit 15% use both Instagram and TikTok 10% use both Reddit and TikTok 5% use all three What percentage of people use at least one of the three apps?

View Explanation

Log in for full answers

Similar Questions

Sample Numeric Answer Question There are 12 people in a room. Six people are wearing socks and four people are wearing shoes; three people are wearing both. How many are in bare feets?

Sample Numeric Answer Question There are 12 people in a room. Six people are wearing socks and four people are wearing shoes; three people are wearing both. How many are in bare feet?

In a group of 50 students: - 20 like hiking - 25 like biking - 10 like both How many like either hiking or biking?

If a class of 40 students includes 18 who play basketball and 15 who play football, with 7 playing both, how many students play at least one of the sports?

30 people were surveyed about their favourite type of pet: 15 people liked cats, 20 people liked dogs and 10 people liked both. Determine how many people liked dogs or cats:(I:1)

In set theory, which is the correct formula for the Principal of Inclusion and Exclusion: (K:1)

30 people were surveyed about their favourite type of pet: 15 people liked cats, 20 people liked dogs and 10 people liked both. Determine how many people liked dogs or cats:(I:1)

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler