three critics review a book. Odds in favour are 5:2, 4:3 and 3:4 respectively for the three critics. find the probability that majority are in the favour of the book

Let the critics be E1, E2, E3.P(E1), P(E2), P(E3) are the probabiities of E1, E2, E3 to be in favour of book.Odds in favour of book for critics E1, E2, E are 5:2, 4:3, 3:4 respectivey.P(E1) = 55+2=57P(E2) = 44+3=47P(E3) = 33+4=37Event of majority being in favour = event of atleast 2 critics being in favour.
Required probability =P(E1E2E3) +P(E1E2E3) +P(E1E2E3)+P(E1E2E3)=57×47×(1-37) + 57×(1-47)×37 +(1-57)×47×37+57×47×37) =57×47×47 +57×37×37+27×47×37+57×47×37=80343+45343+24343+60343=209343

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