7.
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7. Group Membership 2
A poll was taken for music genre preference. Each respondent selected at least one genre. Given the following information, what percentage of people like all three genres?
- 48% selected pop.
- 56% selected jazz.
- 64% selected rock.
- 26% selected pop and jazz.
- 28% selected jazz and rock.
- 24% selected pop and rock.
Pick ONE option
Show answer & explanation
Answer: D. D) 10
Using Inclusion-Exclusion: 100 = 48 + 56 + 64 - (26 + 28 + 24) + x => 100 = 168 - 78 + x => 100 = 90 + x => x = 10%.
Step-by-step Derivation:
Step 1: P(A U B U C) = 100%.
Step 2: Sum of individual sets = 48 + 56 + 64 = 168.
Step 3: Sum of pairwise intersections = 26 + 28 + 24 = 78.
Step 4: 100 = 168 - 78 + x = 90 + x => x = 10.