Question 938149: a manufacturer knows that in a box of 120 light bulbs there will be 3 defective bulbs. Ben picks 2 bulbs from the box. determine the probability that he will pick a) 2 defective bulbs and b) exactly 1 defective bulb.
.. please help.. assigment is due tomorrow, test in 2 days and i cant figure out the answer to these kinda questions. i tried everything but i dont know where to even start with this type of question.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  of the bulbs are defective,
so the probability of Ben's first pick being defective is  ,
and the probability of Ben's first pick being good is  .
a) If Ben's first pick is defective,
he will have 119 light bulbs for his second choice,
and 2 of those will be defective.
So, the probability of picking a second defective bulb after picking the first defective bulb is
 .
All in all, the probability that Ben will pick 2 defective bulbs is
 .
That is about  .
On the other hand, if Ben's first pick is a good bulb,
he will have 119 bulbs to choose from, 3 of them defective, along with  good bulbs.
So, the probability of Ben picking a second good bulb after picking the first good bulb is  .
All in all, the probability that Ben will pick 2 good bulbs is
 .
b) If Ben's chosen bulbs are neither both defective, nor both good bulbs, Ben will have picked exactly 1 defective bulb.
The probability of that is  .
That is about  .
Another way to get at the part b) answer is adding up
the probability of first bulb defective, second bulb good, plus
the probability of first bulb good, second bulb defective.
That would be
When two ways to solve the problem yield the same result, I am happy.
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