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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?









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Option(A) is correct

The probability that Sumit actually sees a Shark, given that he claimed to have seen one.

\(=\dfrac{P(\text{He actually sees the shark and reports truth})}{P(\text{He claims of seeing a shark})}\)

\(=\dfrac{P(\text{Sees the shark}) P(\text{Reports Truth}) }{P(\text{He sees a shark}) P\text{(reports truth}) + P(\text{Doesn't see}) \ P(\text{reports false) }}\)

\(=\dfrac{1/8\times 1/6}{1/8\times 1.6+7/8\times 5/6}\)


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