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What difference does it makes if the same experiment is conducted with a transparent box? I mean what is the significant of the opaque box in the original thought experiment? Can't we observe the radioactive decay in progress? Isn't this experiment about the probabilistic nature of particle decaying?

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The idea is that Schrodinger's cat must be perfectly isolated from all outside influence. That's why it's imagined as being put in a box to begin with, as opposed to say the guy (Schrodinger?) watching it just turning his back. By definition, a transparent box is one which admits a particular outside influence - namely, light - to enter into it, and thus it would disturb the extremely delicate, macroscopic quantum state held within. In fact, no box perfect enough to do the job with a real cat (or cat-sized physical system to avoid the obvious animal cruelty) is possible. If nothing else, heat will be conducted and radiated from the cat to the box and then on to the outside world, and that will leak information, and there is no way to make this transfer mathematically zero. The best we've managed to do in real experiments is I believe with small cantilevers just on the edge of visibility to the naked eye, and with coherence times (lifetime of non-trivial quantum state) on the order of nanoseconds - long enough to be detectable with sensitive equipment, but far below the limits of human perception.

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Not knowing the decay time, we can use a transparent box and a lot of cats to get a statistics of the mean decay time. After this experiment we could open a opaque box using the statistical evaluated time and after a lot of cats we will get the result, that in 50% the cat is death.

For the description of the situation in a opaque box we use a probalistic equation which describes the lack of knowlede about the real state inside the box.

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