Three critics review a book. For the three critics, the odds in favour of the book are (5: 2),(4: 3) and (3: 4) respectively. The probability that the majority is in favour of the book is

Step-by-step solution

P (C₁ )= 5 5+2 = 5 7 , P (C₂ )= 4 4+3 = 4 7 , P (C₃ )= 3 3+4 = 3 7 now, required probability aligned & =P (C₁ ) P (C₂ ) P ( C ₃ )+P ( C ₁ ) P (C₂ ) P (C₃ )+P (C₁ ) P ( C ₂ ) P (C₃ )+P (C₁ ) P (C₂ ) P (C₃ ) & = 5 7 4 7 4 7 + 2 7 4 7 3 7 + 5 7 3 7 3 7 + 5 7 4 7 3 7 & = 80+24+45+60 343 = 209 343 aligned