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Homework Help: Probability that a chip is operative

  1. Jul 25, 2010 #1
    1. The problem statement, all variables and given/known data
    A chip contains twenty identical transistors, which are connected in such a way
    that the chip will perform its function provided that no more than three of the
    transistors have failed. The probability that any given transistor has failed
    equal 0.1. Calculate the probability that the chip is operative.

    3. The attempt at a solution
    [tex]\sum_{n=0}^{3}\binom{20}{n} 0.1^{n} (1-0.1)^{20-n}[/tex]

    But this can not be right since the probability that the chip is still working
    is higher with less transistors but with the same failed number.

    20 transistors p = 0.8670
    10 transistors p = 0.9872

    Can someone give me a hint please.
  2. jcsd
  3. Jul 25, 2010 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper
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    I didn't check your calculations, but your approach is correct. Your result is actually reasonable. When you have 20 transistors, there are many more ways to have up to 3 fail than when you have only 10 transistors.
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