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It should be Prob. of '6' * Prob. of truth = 1/6*3/4=1/8. Aviveksingh222 wrote:A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually six is
1. 1/8
2. 2/8
3. 3/8
4. 1/2
3
Ian, I'm not following your explanation...also, this problem should not be on this forum, as this is data sufficiency, not problem solving...but back to the problem at hand...the problem asks for the probability that this man actually rolled a 6. To calculate that probability, you simply multiply the probability that he is telling the truth (3/4) to the probability of rolling a 6 (1/6) - thus the answer should be 1/8. I feel like you made this problem more complicated than what was asked, but maybe I'm the one missing something.Ian Stewart wrote:Under any reasonable interpretation of the question, the answer should be 3/4. The answer is only equal to 3/8 if you make the ridiculous assumption that every time the man lies, he says "I rolled a six" - that is, the answer is only 3/8 if you assume the man will never lie by saying "I rolled a three" or "I rolled a five". I don't know why you would assume that from the wording of the question, so it's a badly designed question.
But we can answer the question they intended:
* 1/6 of the time the man rolls a six, and 3/4 of those times he tells the truth, so 3/24 of the time, he claims to have rolled a six and is telling the truth
* assuming when he lies he always claims to have rolled a six, then 5/6 of the time the man rolls something other than six, and 1/4 of the time he lies and pretends to have rolled a six, so 5/24 of the time, he claims to have rolled a six and is lying
So when he claims to have rolled a six, the ratio of the times he's telling the truth to the times he's lying is 3/24 to 5/24, or 3 to 5, and the probability he's telling the truth is thus 3/8.
No, you would multiply 3/4 by 1/6 if you wanted to know the probability that he both rolled a six and told the truth about it. That's not what the question asks. Here, all we know is that he reports that he rolled a six. He may have done so and told the truth, or he may have rolled, say, a two and lied. So we need to work out how often, when he actually rolls a six, he reports that he rolled a six, and how often, when he doesn't roll a six, that he claims that he does.cking6178 wrote: To calculate that probability, you simply multiply the probability that he is telling the truth (3/4) to the probability of rolling a 6 (1/6) - thus the answer should be 1/8. I feel like you made this problem more complicated than what was asked, but maybe I'm the one missing something.
In case my post above was unclear, it might be easier to see why it is incorrect to simply multiply those two probabilities by looking at a simpler example, since the dice example is not at all intuitive. Suppose a man who lies 1/2 the time flips a coin, and tells you he got Heads. What's the probability he actually got Heads? If you just multiply the probability of getting Heads by the probability this man tells the truth, you'd think the answer is 1/4 here, but it's not.cking6178 wrote:
To calculate that probability, you simply multiply the probability that he is telling the truth (3/4) to the probability of rolling a 6 (1/6) - thus the answer should be 1/8. I feel like you made this problem more complicated than what was asked, but maybe I'm the one missing something.
No, you would multiply 3/4 by 1/6 if you wanted to know the probability that he both rolled a six and told the truth about it. That's not what the question asks. Here, all we know is that he reports that he rolled a six. He may have done so and told the truth, or he may have rolled, say, a two and lied. So we need to work out how often, when he actually rolls a six, he reports that he rolled a six, and how often, when he doesn't roll a six, that he claims that he does.
This question is a conditional probability question, and it is not at all similar to any real GMAT questions I've seen, so I wouldn't worry about it much.
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