A group of 100 college students were asked whether they prefer to listen to musi
ID: 3293456 • Letter: A
Question
A group of 100 college students were asked whether they prefer to listen to music by Phish or the Grateful Dead. Students may choose both, and they may choose neither. The results were: 59 students listen to Phish: 52 students listen to the Grateful Dead: 6 student listen to neither Phish nor the Grateful Dead. Use the Principle of Inclusion/Exclusion to determine the number of students who listen to BOTH Phish and the Grateful Dead. and/or explanations. At the dining center, 150 students were surveyed about their preference for dinner and their choices were beef, chicken, or salmon. Students may indicate a preference for any number of options, including none. The results were: 73 students prefer beef: 85 students prefer chicken: 96 students prefer salmon: 56 students prefer beef and chicken: 37 students prefer beef and salmon: 54 students prefer chicken and salmon: 30 students prefer all three options. Use the Principle of Inclusion/Exclusion to determine the number of students who prefer none of these options. and/or explanations.Explanation / Answer
6 students neither listen to Phish nor Grateful Dead
=> 100 - 6 = 94 of the students listen to at least one of the 2 great bands.
Now,
The number of students listening to at least one of the 2 great bands
= The number of students listening to Phish + The number of students listening to Grateful Dead
- The number of students listening to both of the bands
=>
94 = 59 + 52 - The number of students listening to both of the bands
=>
The number of students listening to both of the bands = 52 + 59 - 94 = 7
The number of students preferring none of the options
= Total Number of Students - The number of students preferring at least one of the options
= Total Number of Students - [ Students preferring beef + Students preferring chicken + Students preferring salmon - Students preferring both beef and chicken - Students preferring both beef and salmon - Students preferring both salmon and chicken + Students preferring all three options ]
= 150 - [ 73 + 85 + 96 - 56 - 37 - 54 + 30 ]
= 13
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