A man is known to speak the truth 3 out of 4 | vedclass

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

Question

(A) Let $E$ be the event that a six occurs and $E'$ be the event that a six does not occur.Let $A$ be the event that the man reports that it is a $6$.

Vedclass · Accepted Answer

$\frac{3}{8}$

Vedclass · Answer

(A) Let $E$ be the event that a six occurs and $E'$ be the event that a six does not occur.Let $A$ be the event that the man reports that it is a $6$.We have $P(E) = \frac{1}{6}$ and $P(E') = 1 - \frac{1}{6} = \frac{5}{6}$.The probability that the man speaks the truth is $P(T) = \frac{3}{4}$,so the probability that he lies is $P(L) = 1 - \frac{3}{4} = \frac{1}{4}$.If a six occurs,the man reports it as a six if he speaks the truth,so $P(A|E) = \frac{3}{4}$.If a six does not occur,the man reports it as a six if he lies,so $P(A|E') = \frac{1}{4}$.Using Bayes' theorem,the probability that it is actually a six given that he reported a six is:$P(E|A) = \frac{P(E) \cdot P(A|E)}{P(E) \cdot P(A|E) + P(E') \cdot P(A|E')}$$P(E|A) = \frac{\frac{1}{6} \cdot \frac{3}{4}}{\frac{1}{6} \cdot \frac{3}{4} + \frac{5}{6} \cdot \frac{1}{4}}$$P(E|A) = \frac{\frac{3}{24}}{\frac{3}{24} + \frac{5}{24}} = \frac{3}{8}$.

$A$ man is known to speak the truth $3$ out of $4$ times. He throws a die and reports that it is a six. The probability that it is actually a six,is

Similar Questions

$A$ lot consists of $12$ good pencils,$6$ with minor defects,and $2$ with major defects. $A$ pencil is chosen at random. The probability that this pencil is not defective is

$10$ coins are tossed. What is the probability that exactly $5$ heads appear?

From a pack of $52$ cards,one card is drawn at random. The probability that it is either a king or a queen is:

If $E$ and $F$ are independent events such that $0 < P(E) < 1$ and $0 < P(F) < 1,$ then

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}$ respectively. The probability of winning by neither of them is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module