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posted by  barb321 on 11/4/2009 10:47:32 PM  |  status: Closed  |  Earned Karma: 325

geometric distribution, geometric progression and logarithms

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Statistics and Probability N/A N/A N/A 11/5/2009 at 7:00:00 PM
Question Details:
In a torture test a switch is turned on and off til it fails. If the probability that a switch will fail any time is 0.001, what is the probability that the switch will fail AFTER it has been turned on or off 1200 times. Assume that the conditions underlying the geometric distribution are met.
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posted by ValdoKan on 11/5/2009 12:14:57 AM  |  status: Live
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Response Details:
p =0.001 the probability that a switch fails
q =1-p = 0.999



===
===== 0.000999
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posted by Orca on 11/5/2009 2:27:29 AM  |  status: Live
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Response Details:
p=.001 Probability switch fails on any trial
q=.999
Let X be the number of trial to the first failure. Then
P(X=k)=pqk-1   k=1,2,.......
Hence
P(X>1200)=1-P(X1200)
Now
=.69899
Therefore
P(X>1200)=1-.69899=.30
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