Question 1158734
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            unlocked / meaning (Dictionary) :   "undo the lock of (something) by using a key"


             * * * Actually,  as formulated,  this text can be interpreted in at least 3 (three) different ways. * * * 



<pre>
Way $1.  The keys are INDISTINGUISHABLE, and the problem asks what is the probability that the door will be open at the third trial.


             (Here I make a sub-assumption, that the person who unlocks, is not a total idiot and KNOWS which two keys of the total 6 keys
             he (or she) used in the first two trials - although 6 keys are indistinguishable).
    


Way #2.  The keys are NUMBERED, 1, 2, 3, 4, 5 and 6 at the ring; the person uses them consequently in this order,
          and the problem asks if the key #3 will unlock the door at the third trial.



Way #3.  The keys are NUMBERED, 1, 2, 3, 4, 5 and 6 at the ring; the person uses them non-necessary in this order, 
         and the problem asks if the key #3 will unlock the door at some trial from the third to sixth.



               Now, if the problem admits so many interpretations, it means ONLY ONE THING:

               the formulation IS NOT a Math problem, at all   (and, in particular, is composed unprofessionally).




In version 1 of the formulation, the answer is  P = {{{1/4}}},  and it is OBVIOUS.


In version 2 of the formulation, the answer is  the same P = {{{1/4}}},  and it is OBVIOUS, too.


In version 3  of the formulation, the question can be reformulated in this way:

    What is the probability that the key #3 is that UNIQUE good key among remaining 4 keys.


    Again, in this case, the probability under the question is  P = {{{1/4}}},
        and it is OBVIOUS, again.
</pre>

Thus, &nbsp;<U>FORTUNATELY</U>, &nbsp;the answer is the same for each and every of these &nbsp;3 &nbsp;interpretations.


Solved, &nbsp;answered and explained in the most thorough way.


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The serious deficiency of this post is in that it &nbsp;<U>DOES &nbsp;NOT &nbsp;describe the probabilistic experiment with thorough precision</U>,
as it is required.



/\/\/\/\/\/\


<U>Post solution note</U>: &nbsp;&nbsp;you may seek, try and use more complicated ways, &nbsp;solutions and models, &nbsp;if you wish.


It will not change the final answer, until your interpretation is under that 3 cases considered above.