Three persons A,B and C attended a recruitmen | vedclass

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

Question

(D) Let the probabilities of $A$,$B$,and $C$ passing the test be $P(T_A) = k$,$P(T_B) = 2k$,and $P(T_C) = 3k$ respectively,based on the ratio $1:2:3$.

Vedclass · Accepted Answer

$\frac{1}{5}$

Vedclass · Answer

(D) Let the probabilities of $A$,$B$,and $C$ passing the test be $P(T_A) = k$,$P(T_B) = 2k$,and $P(T_C) = 3k$ respectively,based on the ratio $1:2:3$. Let $I$ be the event that a person faces the interview successfully. The conditional probabilities are $P(I|T_A) = 0.8$,$P(I|T_B) = 0.7$,and $P(I|T_C) = 0.6$. We need to find the probability that $A$ is selected,given that one of them is selected. This is calculated using Bayes' Theorem: $P(A|I) = \frac{P(T_A) 	imes P(I|T_A)}{P(T_A) 	imes P(I|T_A) + P(T_B) 	imes P(I|T_B) + P(T_C) 	imes P(I|T_C)}$ $P(A|I) = \frac{k 	imes 0.8}{k 	imes 0.8 + 2k 	imes 0.7 + 3k 	imes 0.6}$ $P(A|I) = \frac{0.8k}{0.8k + 1.4k + 1.8k} = \frac{0.8k}{4.0k} = \frac{0.8}{4} = \frac{1}{5}$.

Similar Questions

Bag $A$ contains $3$ white and $7$ red balls,and bag $B$ contains $3$ white and $2$ red balls. One bag is selected at random and a ball is drawn from it. What is the probability that the ball was drawn from bag $A$,given that the ball drawn is white?

$A$ boy speaks the truth in $3$ out of $5$ times. If he throws a die and reports that the number appeared on it is $5$,then the probability that it is actually $5$ is:

$A$ man is known to speak the truth $4$ out of $5$ times. He throws a die and reports that it is a six. The probability that it was actually a six is

Vedclass Test Series

Exam Paper Generator

Online Exam Module