SOLUTION: A box contains 12 light bulbs of which 5 are defective. All the bulbs look alike and have equal probability of being chosen. Three bulbs are picked up at random. What is the probab

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Question 1194843: A box contains 12 light bulbs of which 5 are defective. All the bulbs look alike and have equal probability of being chosen. Three bulbs are picked up at random. What is the probability that at least 2 are defective?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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A box contains 12 light bulbs of which 5 are defective.
All the bulbs look alike and have equal probability of being chosen.
Three bulbs are picked up at random. What is the probability that at least 2 are defective?
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The number of selecting 3 light bulbs from 12 is  C%5B12%5D%5E3 = %2812%2A11%2A10%29%2F%281%2A2%2A3%29 = 220.


It goes to the denominator of the probability as the size of the space events.


The number of selecting 2 or more defective choosing 3 bulbs from 12 is

    C%5B5%5D%5E2%2AC%5B12-5%5D%5E1 + C%5B5%5D%5E3 = 10*7 + 10 = 80.


This number goes to the numerator of the probability as the size of favorable events.


So, the probability is  P = favorable_triples%2Ftotal_triples = 80%2F220 = 4%2F11.    ANSWER

Solved.