SOLUTION: if 2 percent of elective bulbs manufactured by a certain company are defective, find the probability that in a sample space of 200 bulbs less than 2 are defective.

Question 1128409: if 2 percent of elective bulbs manufactured by a certain company are defective,
find the probability that in a sample space of 200 bulbs less than 2 are
defective.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
if 2 percent of elective bulbs manufactured by a certain company are defective,
find the probability that in a sample space of 200 bulbs less than 2 are
defective.

The probability that less than 2 are defective is the probability that
all 200 bulbs are good OR that there is exactly 1 bad bulb and 199 good 
bulbs. 

The probability that a bulb is defective is 0.02,
The probability that a bulb is good is therefore 1.00-0.02 = 0.98,

The probability that all 200 are good is (0.98)²⁰⁰ = 0.0175879466

The probability that the 1st bulb is bad and the 2nd-200th
bulbs are good is (0.02)(0.98)¹⁹⁹ = 0.0003589376858

The probability that the 2nd bulb is bad and the 1st and the 3rd-200th bulbs 
are good is also 0.0003589376858.

...

And it's the same for any 1 bulb being bad, and the other 199 bulbs being
good so the probability is 200 times 0.0003589376858 or 0.0717875372

So adding the probability of 'none bad' and the probability of 'exactly 1 bad'
gives

0.0175879466 + 0.0717875372 = 0.0721464748  <--final answer

Edwin

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