SOLUTION: A box contains 1000 light bulbs. The probability that there is at least 1 defective bulb in the box is 0.1, and the probability that there are at least 2 defective bulbs is 0.05.

Question 1187583: A box contains 1000 light bulbs. The probability that there is at least 1 defective bulb
in the box is 0.1, and the probability that there are at least 2 defective bulbs is 0.05.
Find the probability in each of the following cases:
(a) The box contains no defective bulbs.
(b) The box contains exactly 1 defective bulb.
(c) The box contains at most 1 defective bulb.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The probability that there are no defective bulbs is 0.9, since the rest of the probability (0.1) is devoted to 1 or more defective bulbs.
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that means that the probability of a bulb's not being defective, when raised to the 1000th power, is 0.9
x^1000=0.9
log of both sides and 1000 log x=-0.04576
so log x=0.00004576
raise x to the 10th power
x=0.99989 probably that a given bulb is not defective, so the probability one is defective is 0.0001054
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Exactly 1 defective is
probability exactly 1 is defective is 1000C1*0.99989^999*0.0001054=0.09443
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At most 1 defective is 1- the above probability or 0.90557
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