The probability that A speaks the truth is fr | vedclass

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

Question

(C) Let $P(A)$ be the probability that $A$ speaks the truth and $P(B)$ be the probability that $B$ speaks the truth.Given: $P(A) = \frac{4}{5}$ and $P

Vedclass · Accepted Answer

$\frac{7}{20}$

Vedclass · Answer

(C) Let $P(A)$ be the probability that $A$ speaks the truth and $P(B)$ be the probability that $B$ speaks the truth.Given: $P(A) = \frac{4}{5}$ and $P(B) = \frac{3}{4}$.Then,the probability that $A$ lies is $P(\bar{A}) = 1 - \frac{4}{5} = \frac{1}{5}$.The probability that $B$ lies is $P(\bar{B}) = 1 - \frac{3}{4} = \frac{1}{4}$.They contradict each other if ($A$ speaks the truth and $B$ lies) $OR$ ($A$ lies and $B$ speaks the truth).Required probability $= P(A) 	imes P(\bar{B}) + P(\bar{A}) 	imes P(B)$.$= (\frac{4}{5} 	imes \frac{1}{4}) + (\frac{1}{5} 	imes \frac{3}{4})$.$= \frac{4}{20} + \frac{3}{20} = \frac{7}{20}$.

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?

Similar Questions

If $A$ and $B$ are two independent events,then the probability of occurrence of at least one of $A$ and $B$ is given by $1 - P(A') P(B')$. Is this statement true or false?

$A$ die is thrown. Let $A$ be the event that the number obtained is greater than $3$. Let $B$ be the event that the number obtained is less than $5$. Then $P(A \cup B)$ is

If $A$ and $B$ are independent events such that odds in favour of $A$ is $2:3$ and odds against $B$ is $4:5$,then $P(A \cap B)=$

For two given events $A$ and $B$,$P(A \cap B)$ is:

$A$ card is drawn at random from a well-shuffled deck of $52$ cards. What is the probability that the card is red or a queen?

Vedclass Test Series

Exam Paper Generator

Online Exam Module