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(D) Let $A, B, C$ be the events that the first,second,and third critics favor the book respectively. The probabilities are: $P(A) = \frac{2}{2+5} = \f

Vedclass · Accepted Answer

$\frac{134}{343}$

Vedclass · Answer

(D) Let $A, B, C$ be the events that the first,second,and third critics favor the book respectively. The probabilities are: $P(A) = \frac{2}{2+5} = \frac{2}{7}, P(A') = \frac{5}{7}$ $P(B) = \frac{3}{3+4} = \frac{3}{7}, P(B') = \frac{4}{7}$ $P(C) = \frac{4}{4+3} = \frac{4}{7}, P(C') = \frac{3}{7}$ The majority is in favor if at least two critics favor the book. The probability is $P(A \cap B \cap C') + P(A \cap B' \cap C) + P(A' \cap B \cap C) + P(A \cap B \cap C)$. $= (\frac{2}{7} 	imes \frac{3}{7} 	imes \frac{3}{7}) + (\frac{2}{7} 	imes \frac{4}{7} 	imes \frac{4}{7}) + (\frac{5}{7} 	imes \frac{3}{7} 	imes \frac{4}{7}) + (\frac{2}{7} 	imes \frac{3}{7} 	imes \frac{4}{7})$ $= \frac{18}{343} + \frac{32}{343} + \frac{60}{343} + \frac{24}{343} = \frac{134}{343}$.

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

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