Question

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

Answer 1

Probability of favour p1=5/7,p2=4/7,p3=3/7

Probability that majority in favour of the book=

(1, 2, not3), + ( 1, not2, 3) + (not1, 2 ,3) + (1, 2, 3)

=$(5\ast 4\ast 4+5\ast 3\ast 3+2\ast 4\ast 3+5\ast 4\ast 3)/343$=209/343