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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. * * *
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 = , and it is OBVIOUS.
In version 2 of the formulation, the answer is the same P = , 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 = ,
and it is OBVIOUS, again.
Thus, FORTUNATELY, the answer is the same for each and every of these 3 interpretations.
Solved, answered and explained in the most thorough way.
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The serious deficiency of this post is in that it DOES NOT describe the probabilistic experiment with thorough precision,
as it is required.
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Post solution note: you may seek, try and use more complicated ways, solutions and models, if you wish.
It will not change the final answer, until your interpretation is under that 3 cases considered above.