Q. 55.0( 3 Votes )
A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?
⇒ A speaks truth in 75% of cases
⇒ B speaks truth in 80% of cases
⇒ P(TA) = P(A speaking truth) = 0.75
⇒ P(NA) = P(A not speaking truth) = 1-0.75
⇒ P(NA) = 0.25
⇒ P(TB) = P(B speaking truth) = 0.80
⇒ P(NB) = P(B not speaking truth) = 1-0.80
⇒ P(NB) = 0.20
We need to find the probability for case in which A and B contradict each other for narrating an incident.
This happens only when A not telling truth while B is telling truth and vice-versa.
⇒ P(CAB) = P(A and B contradict each other)
⇒ P(CAB) = P(A tells truth and B doesn’t) + P(B tells truth and A doesn’t)
Since the speaking of A and B are independent events their probabilities will multiply each other.
⇒ P(CAB ) = (P(TA)P(NB)) + (P(NA)P(TB))
⇒ P(CAB) = (0.75×0.20) + (0.25×0.80)
⇒ P(CAB) = 0.15 + 0.20
⇒ P(CAB) = 0.35
∴ The required probability is 0.35.
Rate this question :
A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.RD Sharma - Volume 2
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.Mathematics - Board Papers
A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that one is red and the other is black.RD Sharma - Volume 2
Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1:2:4. The probabilities that A, B and C can introduce changes to improve the profits of the company are 0.8, 0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C.
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.Mathematics - Board Papers
Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. Two balls are transferred at random from BSag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred balls were both black.Mathematics - Board Papers
A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?RD Sharma - Volume 2
Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.RD Sharma - Volume 2
A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?RD Sharma - Volume 2
Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal’s selection is 1/3 and that of Monika’s selection is 1/5. Find the probability that
i. Both of them will be selected
ii. None of them will be selected
iii. At least one of them will be selected
iv. Only one of them will be selected.RD Sharma - Volume 2