From a box containing 8 lamps, 2 of which are lit, we choose three lamps at random.
If X represents burned laps, find the variance of X.
There are some language issues here, as well as a distracting typo. If these lamps are literally lit (e.g. candles with flames), then I am, on one hand, worried that they are lit while in a box, and on the other hand, not surprised by the burned
laps (and hands), as people might accidentally drop them into their laps while taking them out. If "lamp" means electrical lamp of some sort (light bulb, or desk lamp, perhaps), I'm still surprised that they would be lit (turned on) while in storage.
Does "lit" mean formerly used, and "burned" mean the same thing? Or does "burned" mean "burned out", and therefore unable to be lit? We need to know the relationship between these words in order to solve the problem. (It might be helpful to see the problem exactly as you got it, in the original language, so we could better check the meaning.)
In any case, to repeat, we need to see
your thoughts on solving the problem, to see where you need help:
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What probability distributions have you learned about?