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QuestionEncuesta a estudiantes sobre sus preferencias en 3 plataformas: Amazon Prime, HBO y Netflix. Responde:
a.) Estudiantes con las 3 plataformas: b.) Estudiantes con al menos una plataforma: c.) Estudiantes con exactamente una plataforma: d.) Estudiantes con Amazon Prime o HBO, pero no Netflix:

Studdy Solution

STEP 1

Assumptions1. The total number of students is unknown. . The number of students who have Amazon Prime is141.
3. The number of students who do not have Amazon Prime is140.
4. The number of students who do not have HBO is142.
5. The number of students who have Netflix is66.
6. The number of students who do not have Amazon Prime and HBO is66.
7. The number of students who do not have HBO and Netflix is94.
8. The number of students who do not have Amazon Prime and Netflix is112.
9. The number of students who do not have any of these three platforms is46.

STEP 2

First, we need to find the total number of students. We can do this by adding the number of students who have Amazon Prime and the number of students who do not have Amazon Prime.
Total students=Students with Amazon Prime+Students without Amazon PrimeTotal\, students = Students\, with\, Amazon\, Prime + Students\, without\, Amazon\, Prime

STEP 3

Now, plug in the given values for the number of students who have Amazon Prime and the number of students who do not have Amazon Prime to calculate the total number of students.
Total students=141+140Total\, students =141 +140

STEP 4

Calculate the total number of students.
Total students=141+140=281Total\, students =141 +140 =281

STEP 5

To find the number of students who have all three platforms, we subtract the number of students who do not have each platform from the total number of students, then add back the number of students who do not have any platform.
Students with all three=Total students−Students without Amazon Prime−Students without HBO−Students without Netflix+Students without anyStudents\, with\, all\, three = Total\, students - Students\, without\, Amazon\, Prime - Students\, without\, HBO - Students\, without\, Netflix + Students\, without\, any

STEP 6

Plug in the values for the total number of students, the number of students without each platform, and the number of students without any platform to calculate the number of students with all three platforms.
Students with all three=281−140−142−112+46Students\, with\, all\, three =281 -140 -142 -112 +46

STEP 7

Calculate the number of students with all three platforms.
Students with all three=281−140−142−112+46=33Students\, with\, all\, three =281 -140 -142 -112 +46 =33

STEP 8

To find the number of students who have at least one platform, we subtract the number of students who do not have any platform from the total number of students.
Students with at least one=Total students−Students without anyStudents\, with\, at\, least\, one = Total\, students - Students\, without\, any

STEP 9

Plug in the values for the total number of students and the number of students without any platform to calculate the number of students with at least one platform.
Students with at least one=281−46Students\, with\, at\, least\, one =281 -46

STEP 10

Calculate the number of students with at least one platform.
Students with at least one=281−46=235Students\, with\, at\, least\, one =281 -46 =235

STEP 11

To find the number of students who have exactly one platform, we subtract the number of students with all three platforms and the number of students with two platforms from the number of students with at least one platform.
Students with exactly one=Students with at least one−Students with all three−∗(Students without one)Students\, with\, exactly\, one = Students\, with\, at\, least\, one - Students\, with\, all\, three -*(Students\, without\, one)

STEP 12

Plug in the values for the number of students with at least one platform, the number of students with all three platforms, and the number of students without one platform to calculate the number of students with exactly one platform.
Students with exactly one=235−33−2∗(66+94+112)Students\, with\, exactly\, one =235 -33 -2*(66 +94 +112)

STEP 13

Calculate the number of students with exactly one platform.
Students with exactly one=235−33−2∗(66+94+112)=58Students\, with\, exactly\, one =235 -33 -2*(66 +94 +112) =58

STEP 14

To find the number of students who have Amazon Prime or HBO but not Netflix, we subtract the number of students who do not have Amazon Prime or HBO from the total number of students, then subtract the number of students who have Netflix.
Students with Amazon Prime or HBO but not Netflix=Total students−Students without Amazon Prime or HBO−Students with NetflixStudents\, with\, Amazon\, Prime\, or\, HBO\, but\, not\, Netflix = Total\, students - Students\, without\, Amazon\, Prime\, or\, HBO - Students\, with\, Netflix

STEP 15

Plug in the values for the total number of students, the number of students without Amazon Prime or HBO, and the number of students with Netflix to calculate the number of students with Amazon Prime or HBO but not Netflix.
Students with Amazon Prime or HBO but not Netflix=281−66−66Students\, with\, Amazon\, Prime\, or\, HBO\, but\, not\, Netflix =281 -66 -66

STEP 16

Calculate the number of students with Amazon Prime or HBO but not Netflix.
Students with Amazon Prime or HBO but not Netflix=281−66−66=149Students\, with\, Amazon\, Prime\, or\, HBO\, but\, not\, Netflix =281 -66 -66 =149a.) The number of students who have all three platforms is33. b.) The number of students who have at least one of these three platforms is235. c.) The number of students who have exactly one of these three platforms is58. d.) The number of students who have Amazon Prime or HBO but not Netflix is149.

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