lugligino
New member
- Joined
- Jun 13, 2013
- Messages
- 11
10% of a stock of 1000 light bulbs are faulty. If you randomly choose a sample of 10 light bulbs, what is the probability that one is faulty?
I tried this:
There are ten possible events:
1) I choose the faulty bulb at the first attempt.
2) I choose the faulty bulb at the second attempt.
...
10) I choose the faulty bulb at the tenth attempt.
By definition, the probability P1 to immediately choose the first faulty bulb is 10%.
The P2 probability of encountering a defective bulb at the second choice is (900/1000) * (100 / (1000-1)).
The P3 probability of encountering a defective bulb at the third choice is (900/1000) * ((900-1) / (1000-1)) * (100 / (1000-2)).
...
The probability P10 to meet a defective light bulb at the tenth choice is (900/1000) * ((900-1) / (1000-1)) * ((900-2) / (1000-2)) * ... * ((900-8) / (1000-8)) * (100 / (1000-9))
Summing up the probabilities of the ten independent events obtained above I get a 65.3% chance that it seems to be too high. Where am I wrong?
I tried this:
There are ten possible events:
1) I choose the faulty bulb at the first attempt.
2) I choose the faulty bulb at the second attempt.
...
10) I choose the faulty bulb at the tenth attempt.
By definition, the probability P1 to immediately choose the first faulty bulb is 10%.
The P2 probability of encountering a defective bulb at the second choice is (900/1000) * (100 / (1000-1)).
The P3 probability of encountering a defective bulb at the third choice is (900/1000) * ((900-1) / (1000-1)) * (100 / (1000-2)).
...
The probability P10 to meet a defective light bulb at the tenth choice is (900/1000) * ((900-1) / (1000-1)) * ((900-2) / (1000-2)) * ... * ((900-8) / (1000-8)) * (100 / (1000-9))
Summing up the probabilities of the ten independent events obtained above I get a 65.3% chance that it seems to be too high. Where am I wrong?
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