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

(D) The probability that the first critic favours the book is $P(A) = \frac{2}{2+5} = \frac{2}{7}$.$	herefore P(A') = 1 - \frac{2}{7} = \frac{5}{7}$.

Vedclass · Accepted Answer

$\frac{134}{343}$

Vedclass · Answer

(D) The probability that the first critic favours the book is $P(A) = \frac{2}{2+5} = \frac{2}{7}$.$	herefore P(A') = 1 - \frac{2}{7} = \frac{5}{7}$.The probability that the second critic favours the book is $P(B) = \frac{3}{3+4} = \frac{3}{7}$.$	herefore P(B') = 1 - \frac{3}{7} = \frac{4}{7}$.The probability that the third critic favours the book is $P(C) = \frac{4}{4+3} = \frac{4}{7}$.$	herefore P(C') = 1 - \frac{4}{7} = \frac{3}{7}$.Majority will be in favour of the book if at least two critics favour the book.Hence,the probability is $P(A \cap B \cap C') + P(A \cap B' \cap C) + P(A' \cap B \cap C) + P(A \cap B \cap C)$.$= P(A) \cdot P(B) \cdot P(C') + P(A) \cdot P(B') \cdot P(C) + P(A') \cdot P(B) \cdot P(C) + P(A) \cdot P(B) \cdot P(C)$.$= \left(\frac{2}{7} 	imes \frac{3}{7} 	imes \frac{3}{7}ight) + \left(\frac{2}{7} 	imes \frac{4}{7} 	imes \frac{4}{7}ight) + \left(\frac{5}{7} 	imes \frac{3}{7} 	imes \frac{4}{7}ight) + \left(\frac{2}{7} 	imes \frac{3}{7} 	imes \frac{4}{7}ight)$.$= \frac{18}{343} + \frac{32}{343} + \frac{60}{343} + \frac{24}{343} = \frac{134}{343}$.

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

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

Similar Questions

If the odds against solving a question by three students are $2:1$,$5:2$,and $5:3$ respectively,then the probability that the question is solved by only one student is

If the odds in favour of an event be $3 : 5$,then the probability of non-occurrence of the event is

$A$ card is drawn from a pack of $52$ cards. $A$ gambler bets that it is a spade or an ace. What are the odds against his winning this bet?

What is the probability of drawing either a queen or a red card from a deck of $52$ cards?

$A$ random variable $X$ has the probability distribution:
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

For the events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,then $P(E \cup F)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module