in a tv survey it was found that 60% of the viewers watch program A,50%watch program B,47%watch program C,28%watch program - Maths - Sets

Question

in a tv survey it was found that 60% of the viewers watch program
A,50%watch program B,47%watch program C,28%watch program Aand B,23%
watch program A and C,18%watch program B and C 8%watch all the the
three find 1) what percentage of viewers watch programmes A and B
but not C? 2) what percentage of viewers watch exactly two
programmes ? 3) what percentage of viewers do not watch any of
these programmes

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Let number of people be 100
According to question:nA=60nB=50nC=47nA∩B=28nA∩C=23nB∩C=18nA∩B∩C=8Number of viewers who watch atleast one of A, B or C is given by nA∪B∪CWe know that:nA∪B∪C=nA+nB+nC-nA∩B-nA∩C-nB∩C+nA∩B∩C=60+50+47-28-23-18+8=96Hence number of viewers who don't watch any of A,B or C=100-96=4⇒Percentageof viewers who don't watch any of A,B or C=4% Answer 3
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_566d27cac959a%20jpg"
style="width: 189px; height: 154px;">
Now observe Venn Diagram
Number of viewers who watch programmes A and B but not C=nA∩B-nA∩B∩C=28-8=20⇒Percentage of viewers who watch programmes A and B but not C=20%Number of viewers who watch exactly 2 programmes=nA∩B+nA∩C+nB∩C-3×nA∩B∩C=28+23+18-3×8=45⇒Percentage of viewers who watch exactly 2 programmes=45%
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