Uh. Hmm, well, uh, I don't know where he's not

Logic Level 3

If I told you "I lie 75% of the time", what is the probability that I'm actually lying?

There is insufficient information

\frac13

\frac34

\frac23

\frac12

\frac14

2 solutions

Kïñshük Sïñgh
Jul 10, 2015

Speaker lies 75% of the time but this information is given by the speaker only, so we actually can't determine the probability.

Nice_onexD

Moderator note:

You could phrase your solution better.

You should say that because we don't know whether the speaker is telling the truth at that instance, we can't determine the truth of his statement based on that information alone.

Bonus question : Can the probability be 0%? How about 100%? Why or why not?

Could it not be $\frac{1}{2}$ since he's either lying when he says that, or he's not?

Feathery Studio - 5 years, 11 months ago

No, because we don't have any specified information about whether the speaker is lying or not.

Kïñshük Sïñgh - 5 years, 11 months ago

why would we need specified information more than the number of options? the speaker is either lying or telling the truth. regardless of how much the person lies; the fact that they acknowledge they lie means they are equally lying or telling the truth in any given circumstance.

michael bye - 5 years, 11 months ago

@Michael Bye – May be you are right, but what I understand about the question is that speaker said he lies 75% of the time...Focus on the wordings, If I TOLD you ; this means that the speaker has already given the statement, and may be it's possible that he usually say 3/4th times false. Your argument would be correct, had the question - If I tell you, then you can say either he's lying or telling the truth, but question asks for his actual probability of lying...

Kïñshük Sïñgh - 5 years, 11 months ago

Probability could be anything (0 %-100%),as we don't know whether the speaker is telling the truth or not.

Kïñshük Sïñgh - 5 years, 11 months ago

Arulx Z
Jul 14, 2015

What if the speaker is lying about the statement - I lie 75% of the time ?

So what if he is lying? We can only conclude that "I don't lie 75% of the time*.

Pi Han Goh - 5 years, 11 months ago

But since he's lying, the number need not be true. So if he's lying about the statement I lie 75% of the time , his actual lying percent can be anywhere between 0%-100% and conversely, his truth percent can also be between 0%-100%.

Arulx Z - 5 years, 11 months ago

If the probability of him lying = 0% then he always tells the truth, so the line "I lie 75% of the time" means that I lied ==> contradiction.

So the probability is non-zero and can be 100% as well.

Pi Han Goh - 5 years, 11 months ago

@Pi Han Goh – Yes you are correct. It can't be zero.

By the way, can you please check out this note? - Rubiks Cube

I posted it 2 weeks ago but I haven't got any answer yet.

Arulx Z - 5 years, 11 months ago

@Arulx Z – I can't be 100% percent correct. But I'm pretty sure you need to utilize group theory to solve this (which I know nearly nothing). And of course, there should be a computer assisted approach.

Agnishom also mentioned the same thing.

In other words, I don't know how to answer this in a sensible manner because I lack the proper knowledge.

Pi Han Goh - 5 years, 11 months ago

@Pi Han Goh – Okay. Thanks for your reply.

Arulx Z - 5 years, 11 months ago

I'm a little confused. If he's telling the truth, then that means he does lie 3/4 of the time and that this statement is in that 1/4 of the time that he does not lie. Therefore there is a 1/4 chance that he is telling the truth. The complement of 1/4 is 3/4, so doesn't that mean that there is a 3/4 chance he is lying? Maybe there's a flaw in my reasoning here. I am a little tired this morning lol.

Tristan Goodman - 1 year, 3 months ago

Uh. Hmm, well, uh, I don't know where he's not

2 solutions

Nice_onexD

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