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.

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Please find below the solution to the asked query:

Let number of people be 100.According to question:nA=60nB=50nC=47nAB=28nAC=23nBC=18nABC=8Number of viewers who watch atleast one of A, B or C is given by nABCWe know that:nABC=nA+nB+nC-nAB-nAC-nBC+nABC=60+50+47-28-23-18+8=96Hence number of viewers who don't watch any of A,B or C=100-96=4Percentageof viewers who don't watch any of A,B or C=4% Answer 3

Now observe Venn Diagram.Number of viewers who watch programmes A and B but not C=nAB-nABC=28-8=20Percentage of viewers who watch programmes A and B but not C=20%Number of viewers who watch exactly 2 programmes=nAB+nAC+nBC-3×nABC=28+23+18-3×8=45Percentage of viewers who watch exactly 2 programmes=45%
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