A box of 10 light bulbs, 2 of which are faulty. A bulb is selected at random and put into a socket. If it works it is left there, if it is faulty it is discarded and a new bulb is selected. The process I continued until a bulb which works is found. Determine the probability distribution of X, the number of bulbs tried.
solution
Let the event that a bulb works be a success
X follows a geometric distribution i.e. the number of trials before the first success
The number of possible trials before the first success is
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