Three critics review a book. Odds in favour of the book are 5:2, 4:3and 3:4 respectively for three critics. Find the probability that eh majorityare in favour of the book.A. `35//49`B. `125//343`C. `164//343`D. `209//343`

Three critics review a book. Odds in favour of the book are 5:2, 4:3an

1.	Three critics review a book. Odds in favour of the book are 5:2, 4:3and 3:4 respectively for three critics. Find the probability that eh majorityare in favour of the book.A. `35//49`B. `125//343`C. `164//343`D. `209//343`
Answer» Correct Answer - D The probability that the first critic favours the book is `P(E_(1))=(5)/(5+2) =5/7` The probability that the second critic favours the book is `P(E_(2))=(4)/(4+3)=4/7` The probability that the third cirtic favours the books is `P(E_(3))=(3)/(3+4)=3/7` Majority will be in favor of the book if at least two critics favour the book. Hence the probability is `P(E_(1)nnE_(2)nnbarE_(3))+P(E_(1)nnbarE_(2)nnE_(3))` `" "+P(barE_(1)nnE_(2)nnE_(3))+P(E_(1)nnE_(2)nnE_(3))` `=P(E_(1)nnE_(2)barE_(3))P(barE_(3))+P(E_(1))P(barE_(2))P(E_(3))` `" "+P(barE_(1)nnE_(2)nnE_(3))+P(E_(1))P(E_(2))P(E_(3))` `=5/7xx4/7xx(1-(3)/(7))+5/7xx(1-(4)/(7))xx3/7` `" "+(1-(5)/(7))xx4/7xx3/7+5/7xx4/7xx3/7=(209)/(343)`

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Three critics review a book. Odds in favour of the book are 5:2, 4:3and 3:4 respectively for three critics. Find the probability that eh majorityare in favour of the book.A. `35//49`B. `125//343`C. `164//343`D. `209//343`

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