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Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus depot. After three hours,Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times. What is the probability that Sumit actually observed a shark in the waters?
  • a)
    1/36
  • b)
    1/30
  • c)
    5/36
  • d)
    1/24
  • e)
    Inadequate data
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Amit, Sumit and Pramit go to a seaside town to spend a vacation there...
The probability that Sumit actually sees a Shark, given that he claimed to have seen one = P(He actually sees the shark & reports truth) / P(He claims of seeing a shark) =
= [(1/8) X (1/6)] / [(1/8) X (1/6) + (7/8)X(5/6)] = 1/36
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Most Upvoted Answer
Amit, Sumit and Pramit go to a seaside town to spend a vacation there...
Given information:
- Sumit claims to have observed a shark in the waters.
- At that time of the year, only 8 sea-creatures (including a shark) are observable and the probability of observing any creature is equal.
- Sumit has a reputation for not telling the truth 5 out of 6 times.

To find: The probability that Sumit actually observed a shark in the waters.

Analysis:
Let's consider the possible scenarios:
- Sumit observed a shark and told the truth.
- Sumit observed a shark and lied.
- Sumit did not observe a shark and lied.

Since we know that Sumit has a reputation for not telling the truth 5 out of 6 times, the probability of him lying is higher than him telling the truth. Let's calculate the probability of each scenario:

- Probability of Sumit observing a shark and telling the truth = 1/8 * 1/6 = 1/48
- Probability of Sumit observing a shark and lying = 1/8 * 5/6 = 5/48
- Probability of Sumit not observing a shark and lying = 7/8 * 5/6 = 35/48

The total probability of Sumit claiming to have observed a shark is the sum of the first two scenarios:

- Probability of Sumit claiming to have observed a shark = 1/48 + 5/48 = 6/48 = 1/8

Using Bayes' theorem, we can calculate the probability of Sumit actually observing a shark given that he claimed to have observed one:

- Probability of Sumit actually observing a shark = (Probability of Sumit observing a shark and telling the truth) / (Probability of Sumit claiming to have observed a shark)
- Probability of Sumit actually observing a shark = (1/48) / (1/8) = 1/6 * 8/1 = 1/48

Therefore, the probability that Sumit actually observed a shark in the waters is 1/48, which is option A.
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Directions: Analyze the following passage and provide appreciate answers for the questions that follow.Ideas involving the theory probability play a decisive part in modern physics. Yet we will still lack a satisfactory, consistence definition of probability; or, what amounts to much the same, we still lack a satisfactory axiomatic system for the calculus of probability. The relations between probability and experience are also still in need of clarification. In investigating this problem we shall discover what will at first seem an almost insuperable objection to my methodological views. For although probability statements play such a vitally important role in empirical science, they turn out to be in principle impervious to strict falsification. Yet this very stumbling block will become a touchstone upon which to test my theory, in order to find out what it is worth. Thus, we are confronted with two tasks. The first is to provide new foundations for the calculus of probability. This I shall try to do by developing the theory of probability as a frequency theory, along the lines followed by Richard von Mises, But without the use of what he calls the 'axiom of convergence'(or 'limit axiom') and with a somewhat weakened 'axiom of randomness' The second task is to elucidate the relations between probability and experience. This means solving what I call the problem of decidability statements. My hope is that the investigations will help to relieve the present unsatisfactory situation in which physicists make much use of probabilities without being able to say, consistently, what they mean by 'probability'.Q. The statement, "The relations between probability and experience are still in need of clarification" implies that

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Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus depot. After three hours,Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times. What is the probability that Sumit actually observed a shark in the waters?a) 1/36b) 1/30c) 5/36d) 1/24e) Inadequate dataCorrect answer is option 'A'. Can you explain this answer?
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Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus depot. After three hours,Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times. What is the probability that Sumit actually observed a shark in the waters?a) 1/36b) 1/30c) 5/36d) 1/24e) Inadequate dataCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus depot. After three hours,Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times. What is the probability that Sumit actually observed a shark in the waters?a) 1/36b) 1/30c) 5/36d) 1/24e) Inadequate dataCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus depot. After three hours,Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times. What is the probability that Sumit actually observed a shark in the waters?a) 1/36b) 1/30c) 5/36d) 1/24e) Inadequate dataCorrect answer is option 'A'. Can you explain this answer?.
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