Question

A student at a university has been doing a project to investigate entertainment habits of students. They have surveyed 100 random students who were each asked three questions: Have you watched a movie in the last week? Have you listened to music in the last week? Have you read a book in the last week? However, the student keeps a very messy room and has lost some of the results. They have been able to find the following results: Of all the students surveyed, 47 had watched a movie, 37 had listened to music and 43 had read a book in the last week. Also: 8 students answered yes to all three questions 11 students answered yes to questions 1 and 2 only 11 students answered yes to questions 1 and 3 only 17 students answered yes only to question 1 21 students answered no to all three questions Find the missing information and answer the following questions regarding the group surveyed. Give your answers as whole numbers. Calculate the number of students that:

A student at a university has been doing a project to investigate entertainment habits of students. They have surveyed 100 random students who were each asked three questions: 1. Have you watched a movie in the last week? listened to music in the last week? 2 H 3. Have you read a book in the last week? However, the student keeps a very messy room and has lost some of the results. They have been able to find the following results: Of all the students surveyed, 47 had watched a movie, 37 had listened to music and 43 had read a book in the last week. Also: 8 students answered yes to all three questions 11 students answered yes to questions 1 and 11 students answered yes to questions 1 and 17 students answered yes only to question 1 21 students answered no to all three questions only only Find the missing information and answer the following questlons regarding the group surveyed. Give your answers as whole numbers. Calculate the number of students that: but no to question 1 a) answered yes to question 2 or b) answered yes to exactly two questions = c) had watched a movie or read a book but had not listened to music

Answer 1

answered we answered let A be the event that Students had watched a movie make B = be the event that students had listened Canswered rose to musie.) tip ble answere le tribe tine, event that students and read book. M(A) = no. of students under the event A 47 X bizitz ari Die Similarly n(B) = 37 , ncc2743 ncanBne) = 8 globuh;CA MB) = OR IN CAMBRE)= 17. BA e n Cane):-)! ni AnBene')=21 as here are here to calculate ordering nc An(Bue)) onceanB) u Aene)). én caeng) unca qe) Canis ne) @ [w n CAUB) = n(A)+" (B)-1(ANB)], o No oas acanB) 20 de ma n(B) = 37 then in caenB)'inCAO3) = n(s) hay nCOonB) = 37-4 Again nckene) = n(e) anane) +43-0 =32 Scanned with Si CamScanner x tiel

Nori nca nenes) en (Ansone) = n(B9ne). 3 21717 in (eenee :: 38 = n(BUC) 7 atas total ho. of student =1007 2 nl Bue) = 100-38. Ca then n/BUC). = 62 P 100-nl BVC) flori necue) = n(B) i nie)-n(Abne) -) 62 - 37+43 -1 (Bne) L =) n(Bne) = 80-62 = 18 then ncombre) in CARB ne) = 18 a) nCan Bre) = 18-8-10 80 @ we get Incarn (Bue)) = 926432-10 - 58 -10.. 48 b> no. of student answer exactly two question en 2002 to ente) EncanBne) nCane OBC) en Can Breg Now we know that IncanBne) in lanenbe) = n cane) - 8t n canenbe)= IL **-) Scanneh Ganense) -11-8 - 3 Sincane OBIE. . CamScanner

Again | MC AO BOC) + m(Ao boc) - DCAO 8) = nCanB Dee) = 11-8-3 By @@ we get ncaņene"), in Canbene) In Cambo) E 3+3+ 10 =16 octobre PAS -C) to here. We have to find a L9013ncanense) lova a from previons result we get e in Canbene)- 3 CS Scanned with f i re CamScanner