A survey of recent high school graduates regarding literature that they studied

Question

A survey of recent high school graduates regarding literature that they studied during their high school career yielded the following information: 571 read Gone with the Wind, 881 read Moby Dick, 461 read Lord of the Flies, 111 read all three, 31 read none, 73 read only Gone with the Wind, 182 read Gone with the Wind and Lord of the Flies, and 212 read Lord of the Flies and Moby Dick, but not Gone with the Wind. What percent of the recent graduates read exactly one book? Round your answer to the nearest tenth, if necessary.

Explanation / Answer

let read gone with the wind A =571

moby dick B =881

lord of the flies =461

AnBnC =111

(AUBUC)c =31

P(AnC) =182

P(BnC) =212

as An(BcnC) =AnC -AnBnC =182-111 =71

and Bn(CnAc) =BnC -AnBnC =212-111 =101

therefore An(BnCc) =A -AnC) =571-182=389

hence people who read only moby dick =(B) -An(BnCc) -Bn(CnAc) -AnBnC =881-389-101-111 =280

and people who read only moby dick =C -An(BcnC) -BnC =461-71-212 =178

hence people who read exactly one book =280+178+73 =531

total number of people in sample =73+178+280+389+71+101+111+31 =1234

hence  percent of the recent graduates read exactly one book =(531/1234)*100 =43.0%

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