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)
1/36
b)
1/30
c)
5/36
d)
1/24
e)
Inadequate data

Correct answer is option 'A'. Can you explain this answer?

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Most Upvoted Answer

Amit, Sumit and Pramit go to a seaside town to spend a vacation there...

Given:
- Sumit claims to have 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.
- Sumit has a reputation for not telling the truth five out of six times.

To find:
- Probability that Sumit actually observed a shark in the waters.

Solution:
Let us first calculate the probability of Sumit telling the truth and the probability of him lying.
- Probability of Sumit telling the truth = 1/6
- Probability of Sumit lying = 5/6

If Sumit observed a shark:
- Probability that he tells the truth = 1/6
- Probability that he lies = 5/6

If Sumit did not observe a shark:
- Probability that he tells the truth = 5/6
- Probability that he lies = 1/6

Let S be the event that Sumit observed a shark.
Let T be the event that Sumit tells the truth.

We need to find the probability of S given that Sumit claimed to have observed a sea-creature.

Using Bayes' Theorem:
P(S | T) = P(T | S) * P(S) / P(T)

We have:
- P(T | S) = 1/6 (Probability that Sumit tells the truth if he observed a shark)
- P(S) = 1/8 (Probability of observing a shark out of the 8 observable sea-creatures)
- P(T) = P(T | S) * P(S) + P(T | not S) * P(not S)
- P(T | not S) = 5/6 (Probability that Sumit lies if he did not observe a shark)
- P(not S) = 7/8 (Probability of not observing a shark out of the 8 observable sea-creatures)
- P(T) = (1/6 * 1/8) + (5/6 * 7/8) = 29/48

Therefore,
P(S | T) = (1/6 * 1/8) / (29/48)
= 1/36

Hence, the probability that Sumit actually observed a shark in the waters is 1/36. Answer is option (a).

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Community 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) =

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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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