Susan S.

asked • 03/07/16

Find the probability.

The computer repairman is given 7 computers to fix. He knows that there are 3 bad video cards and 5 failed hard drives. What is the probability that the first computer he tries has both problems?

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Candace S. answered • 03/07/16

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Hi Susan,
 
 
          The computer repairman is given 7 computers to fix. He knows that there are 3 bad video cards and 5 failed hard drives. What is the probability that the first computer he tries has both problems?
 
 
 
It is helpful for questions like these to draw a Venn diagram.  One large rectangle with two overlapping circles inside.
 
You are given that there are 3 bad video cards and 5 failed hard drives.
Since 3+5=8 and he only has 7 computers to fix, there must be one computer that has both problems
 
ANSWER:  1/7
 
Hope this helps you with the process.
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Kenneth S.

Very good analysis, Candace. The usual probability tree approach does not work because although you can begin with 2 branches based on Video Good or Bad (with respective counts of 3 and 4 respectively, the second stage (for hard drive) would have only three branches.
 
These would be HD Good / HD Bad, coming off the Video Good branch.  Then, coming off the Video Good branch, there could only be one second stage branch, for HD Bad. But you have 5 bad Videos, but you would not know how to split up the 5 Bads over the two possible HD Bad branches.
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03/07/16

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