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

Step-by-step solution

The probability that the first critic favors the book is P ( A )= 2 2+5 = 2 7 P ( A ^ )=1- 2 7 = 5 7 The probability that the second critic favors the book is P ( B )= 3 3+4 = 3 7 P ( B ^ )=1- 3 7 = 4 7 The probability that the third critic favors the book is P ( C )= 4 4+3 = 4 7 P ( C ^ )=1- 4 7 = 3 7 Majority will be in favor of the book if at least two critics favor the book. Hence, the probability is aligned & P ( A B C ^ )+ P ( A B ^ C ) & + P ( A ^ B C )+ P ( A B C ) & = P ( A ) P ( B ) P ( C ^ )+ P ( A ) P (