The probabilities that A and B speak the trut | vedclass

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

Question

(D) 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

(D) 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 $P(B) = \frac{3}{4}$. The probability that $A$ does not speak the truth is $P(\overline{A}) = 1 - P(A) = 1 - \frac{4}{5} = \frac{1}{5}$. The probability that $B$ does not speak the truth is $P(\overline{B}) = 1 - P(B) = 1 - \frac{3}{4} = \frac{1}{4}$. They contradict each other if one speaks the truth and the other lies. Thus,the probability of contradiction is $P(A \cap \overline{B}) + P(\overline{A} \cap B) = P(A) \cdot P(\overline{B}) + P(\overline{A}) \cdot P(B)$. Substituting the values: $(\frac{4}{5} 	imes \frac{1}{4}) + (\frac{1}{5} 	imes \frac{3}{4}) = \frac{4}{20} + \frac{3}{20} = \frac{7}{20}$.

The probabilities that $A$ and $B$ speak the truth are $\frac{4}{5}$ and $\frac{3}{4}$ respectively. The probability that they contradict each other when asked to speak on a fact is

Similar Questions

$A$ speaks the truth in $75\%$ of cases and $B$ speaks the truth in $80\%$ of cases. What is the probability that they contradict each other in stating the same fact?

If an integer is chosen at random from the first $100$ positive integers,then the probability that the chosen number is a multiple of $4$ or $6$ 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 $P(A \cap B)=$

If a card is drawn at random from a well-shuffled pack of $52$ playing cards,then the probability that it is either an ace or a spade card is

Given two independent events $A$ and $B$ such that $P(A) = 0.3$ and $P(B) = 0.6$. Find $P(A \text{ or } B)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module