Three critics review a book. For the three cr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $P(C_1), P(C_2), P(C_3)$ be the probabilities that the three critics are in favour of the book. Given the odds in favour are $(5: 2), (4: 3),

Vedclass · Accepted Answer

$\frac{209}{343}$

Vedclass · Answer

(C) Let $P(C_1), P(C_2), P(C_3)$ be the probabilities that the three critics are in favour of the book. Given the odds in favour are $(5: 2), (4: 3), (3: 4)$,we have: $P(C_1) = \frac{5}{5+2} = \frac{5}{7}, P(\bar{C}_1) = \frac{2}{7}$ $P(C_2) = \frac{4}{4+3} = \frac{4}{7}, P(\bar{C}_2) = \frac{3}{7}$ $P(C_3) = \frac{3}{3+4} = \frac{3}{7}, P(\bar{C}_3) = \frac{4}{7}$ For the majority to be in favour,at least two critics must be in favour. Required probability $= P(C_1)P(C_2)P(\bar{C}_3) + P(C_1)P(\bar{C}_2)P(C_3) + P(\bar{C}_1)P(C_2)P(C_3) + P(C_1)P(C_2)P(C_3)$ $= (\frac{5}{7} 	imes \frac{4}{7} 	imes \frac{4}{7}) + (\frac{5}{7} 	imes \frac{3}{7} 	imes \frac{3}{7}) + (\frac{2}{7} 	imes \frac{4}{7} 	imes \frac{3}{7}) + (\frac{5}{7} 	imes \frac{4}{7} 	imes \frac{3}{7})$ $= \frac{80}{343} + \frac{45}{343} + \frac{24}{343} + \frac{60}{343} = \frac{209}{343}$

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

Similar Questions

The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

If $A$ and $B$ are arbitrary events,then

The odds against a person who is $40$ years old living until he is $70$ are $8$ to $5$,and the odds against another person who is $50$ years old living until he is $80$ are $4$ to $3$. Find the probability that exactly one of them will be alive $30$ years from now.

For an event,the odds against are $6 : 5$. The probability that the event does not occur is

If the probability of $A$ failing an exam is $1/5$ and the probability of $B$ failing is $3/10$,what is the probability that either $A$ or $B$ fails?

Vedclass Test Series

Exam Paper Generator

Online Exam Module