Re: Probability of making a choice by a person, on the basis of earlier made choices?
- From: Paul Rubin <rubin@xxxxxxx>
- Date: Tue, 27 May 2008 17:38:33 -0400
Marcin wrote:
We are asking a man a few questions. After every response we can
check, whether he told the truth or deliberately lied. Lets say, at
the beginning, the probability, that the man will lie and the
probability the man will tell the truth are the same (0.5). If the man
answers the first question and lies, the probability that he will also
lie when asking a second question is (I guess) already greater than
0.5.
Why?
But, if the man will answer first five questions frankly, the
probability, that in the reply to sixth question he will also tell the
truth is already much higher than 0.5.
Why?
But how high is the propability
exactly, and how do you calculate that?
(sorry for english :) thx
You need more information.
If the man randomly and independently decides whether to answer each question truthfully, his probability of a lie on question 6 is unaffected by how many lies he told in the first five questions. In this case, the proportion of lies detected among questions whose answers were checked converges to his probability of lying on any given question as the number of questions checked increases (Weak Law of Large Numbers).
On the other hand, it is possible that the man is more (or less) likely to lie immediately after a lie than immediately after a truthful response. In this case his long-term (dare I say steady-state) probability of lying may not be an accurate reflection of what he will say to the next question. As an extreme example, picture someone who strictly alternates between lies and truthful answers. Over the long run, he lies 50% of the time, but if he just lied then his probably of lying on the next question is zero.
/Paul
.
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