Data Sufficiency

viveksingh222 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 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.

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.