Question

A magazine surveyed subscribers asking which of the following reality shows they watched on a regular basis survivor The Voice America’s got talent. The results showed that 359 watched Survivor 298 watched The Voice 285 watched America’s got talent 197 watch Survivor and The Voice 200 watch Survivor and America’s got talent 143 watch The Voice, and America’s got talent 70 watch Survivor, The Voice and America’s got talent and 26 watch none of these shows .

a.) How many subscribers were surveyed?

b.)Of the subscribers surveyed, how many watched survivor and americas got talent, but not the voice?

c.) of the subscribers surveyed how many watch The Voice, but neither Survivor nor America’s got talent?

d.) of the subscribers surveyed how many watched exactly 2 of these shows?

e.) of the subscriber surveyed how many watch at least one of these shows?

Answer 1

a.) 982 subscribers were surveyed.

b.) 130 subscribers watched Survivor and America's Got Talent but not The Voice.

c.) 28 subscribers watched The Voice but neither Survivor nor America's Got Talent.

d.) 543 subscribers watched exactly 2 of these shows.

e.) 956 subscribers watched at least one of these shows.

Let S, V, and A represent the number of subscribers who watched Survivor, The Voice, and America's Got Talent, respectively. Also, let SV, SA, VA, and SVA represent the number of subscribers who watched both Survivor and The Voice, Survivor and America's Got Talent, The Voice and America's Got Talent, and all three shows, respectively.

Given data:

S=359

V=298

A=285

SV=197

SA=200

VA=143

SVA=70

None=26

Now, let's find the answers to the questions:

a.) The total number of subscribers surveyed (N) can be found by adding the number of subscribers who watched each show and subtracting those who watched two or more shows, and then adding those who watched all three shows:

N=S+V+A−(SV+SA+VA)+SVA + None

N=359+298+285−(197+200+143)+70+26

N=982

So, 982 subscribers were surveyed.

b.) The number of subscribers who watched Survivor and America's Got Talent but not The Voice (S∩A−(SV+SVA)):

SA−(SVA)=200−70=130

c.) The number of subscribers who watched The Voice but neither Survivor nor America's Got Talent (V−(SV+VA−SVA)):

V−(SV+VA−SVA)=298−(197+143−70)=28

d.) The number of subscribers who watched exactly 2 of these shows (

SV+SA+VA−2SVA): 197+200+143−2×70=543

e.) The number of subscribers who watched at least one of these shows (N−None):982−26=956