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The odds that Amit speaks the truth are 1:2 and the odds that Bunty speaks the truth are 2:3. What is the probability that exactly one of Amit and Bunty is telling the truth? 
  • a)
    3/5 
  • b)
    4/15 
  • c)
    7/15 
  • d)
    4/7 
  • e)
    3/7
Correct answer is option 'C'. Can you explain this answer?
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The odds that Amit speaks the truth are 1:2 and the odds that Bunty sp...
Question Analysis:
In this question, we are given the odds of Amit and Bunty speaking the truth. We are asked to find the probability that exactly one of them is telling the truth.

Given information:
- The odds that Amit speaks the truth are 1:2.
- The odds that Bunty speaks the truth are 2:3.

Approach:
To solve this problem, we can use the concept of odds and convert the odds to probabilities.
We will calculate the probability that Amit is telling the truth and Bunty is lying, and then the probability that Amit is lying and Bunty is telling the truth. Finally, we will add these two probabilities to get the probability that exactly one of them is telling the truth.

Solution:
Step 1: Calculate the probability that Amit is telling the truth and Bunty is lying.
The odds that Amit speaks the truth are 1:2. This means that the probability of Amit telling the truth is 1/(1+2) = 1/3.
The odds that Bunty speaks the truth are 2:3. This means that the probability of Bunty lying is 3/(2+3) = 3/5.
Therefore, the probability that Amit is telling the truth and Bunty is lying is (1/3) * (3/5) = 1/5.

Step 2: Calculate the probability that Amit is lying and Bunty is telling the truth.
The probability that Amit is lying is 1 - 1/3 = 2/3.
The probability that Bunty is telling the truth is 2/(2+3) = 2/5.
Therefore, the probability that Amit is lying and Bunty is telling the truth is (2/3) * (2/5) = 4/15.

Step 3: Calculate the probability that exactly one of Amit and Bunty is telling the truth.
The probability that exactly one of them is telling the truth is the sum of the probabilities calculated in Step 1 and Step 2.
Therefore, the probability that exactly one of Amit and Bunty is telling the truth is 1/5 + 4/15 = 7/15.

Answer:
Therefore, the probability that exactly one of Amit and Bunty is telling the truth is 7/15. Hence, the correct answer is option C.
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Directions: Answer the questions based on the following passage.Ludwig Wittgenstein asserted that with the publication of his Tractatus Logico-Philosophicus he had solved all philosophical problems and retired to teach mathematics at the secondary level. He believed he had achieved this through his exploration of the logic of language, which he referred to as his “picture theory” of language.Wittgenstein’s contention was that the world consisted of a collection of interconnected “facts” that created “pictures” of the world through propositions. These propositions are meaningful if they picture matters of empirical fact, such as “Meri is six feet tall.” In order for these linguistic pictures to accurately represent facts, they must have the same logical structure as matters of empirical fact.The problem is that philosophical propositions, such as “truth is beauty,” are not matters of empirical fact. Since language itself is based on this relationship, philosophers cannot extricate themselves from the realm of language in order to actually say anything about whether or not the “pictures” have the same logical structure as the facts. One important consequence of this argument is that it is nonsensical to discuss philosophical problems. The propositions that philosophers commonly make are not technically wrong but nonsensical. For Wittgenstein, the ultimate goal of philosophy itself is not the actual study or pursuit of “truth.” Philosophy has more to do with clarifying the relationship between language and truth than truth itself. The Tractatus ends up subverting its own claims by concluding that the kind of propositions of which it is composed are senseless.The most commonly quoted excerpt from the book is the proposition “What we cannot speak about we must pass over in silence.”Q. The author believes Wittgenstein would likely agree with which of the following statements?

Directions: Answer the questions based on the following passage.Ludwig Wittgenstein asserted that with the publication of his Tractatus Logico-Philosophicus he had solved all philosophical problems and retired to teach mathematics at the secondary level. He believed he had achieved this through his exploration of the logic of language, which he referred to as his “picture theory” of language.Wittgenstein’s contention was that the world consisted of a collection of interconnected “facts” that created “pictures” of the world through propositions. These propositions are meaningful if they picture matters of empirical fact, such as “Meri is six feet tall.” In order for these linguistic pictures to accurately represent facts, they must have the same logical structure as matters of empirical fact.The problem is that philosophical propositions, such as “truth is beauty,” are not matters of empirical fact. Since language itself is based on this relationship, philosophers cannot extricate themselves from the realm of language in order to actually say anything about whether or not the “pictures” have the same logical structure as the facts. One important consequence of this argument is that it is nonsensical to discuss philosophical problems. The propositions that philosophers commonly make are not technically wrong but nonsensical. For Wittgenstein, the ultimate goal of philosophy itself is not the actual study or pursuit of “truth.” Philosophy has more to do with clarifying the relationship between language and truth than truth itself. The Tractatus ends up subverting its own claims by concluding that the kind of propositions of which it is composed are senseless.The most commonly quoted excerpt from the book is the proposition “What we cannot speak about we must pass over in silence.”Q. Based on the context of the passage, the author’s use of the word “empirical” most nearly means which of the following?

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The odds that Amit speaks the truth are 1:2 and the odds that Bunty speaks the truth are 2:3. What is the probability that exactly one of Amit and Bunty is telling the truth?a)3/5b)4/15c)7/15d)4/7e)3/7Correct answer is option 'C'. Can you explain this answer?
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