Question 976066: A company that produces light bulbs records a 1 if a light bulb is defective and a 0 if the lightbulb meets quality standards. Estimate the probability that the next bulb produced will be defective.
0 0 0 0 0 0 0 0 0 0 0
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The issue is that given the first 11 were not defective, so at what point is the probability of a defective light bulb no greater than a certain amount?
The question is basically how likely is it for 11 bulbs chosen at random to be suitable and 1 to be defective?
If the probability is 0.9 that they are suitable, the probability of one out of 12 is not is 12C1 0.9^11 0.1=0.38.
If the probability is 0.995, the chances are 0.057 that one bulb will be chosen defective out of 12.
This doesn't answer the question for an individual light bulb, but it gives a reasonable upper bound for the probability the next one will be defective. It will be low, because 11 in a row have been chosen non-defective.
For the 12th light bulb to be non-defective, I could make the case for zero probability, since I do not yet have any evidence that any are defective. It is much the same as a point estimate. It may not be accurate, but it is the best guess that one has. This is the case here.
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