In a "torture test" a light switch is turned on and off until it fails. If the probability that the switch will fail anytime it is turned on or off is .001
, what is the probability that the switch will fail after it has been turned on or off 1,200
times? Assume that the conditions underlying the geometric distributions are met. [Hint:
use the formula for the value of an infinite geometric progression]

Question

In a "torture test" a light switch is turned on and off until it fails. If the probability that the switch will fail anytime it is turned on or off is .001 
, what is the probability that the switch will fail after it has been turned on or off 1,200
times? Assume that the conditions underlying the geometric distributions are met. [Hint:
use the formula for the value of an infinite geometric progression]

anonymous · Answer

I'm a bit confused on how to go about doing this one. It says I have to use the infinite geometric pregression formula but it isn't mentioned in my book. I was only given the geometric distribution formula: $$g(x;p)=p(1-p)^{x-1} for x=1,2,3,4...$$

anonymous · Answer

I would use binomial distribution.

anonymous · Answer

Okay then but what would n be?

anonymous · Answer

1200.

anonymous · Answer

alright, and p=.001 so would k be 2 since I'm only given 2 options (turning the switch on or off)?

anonymous · Answer

Wait...

anonymous · Answer

Wait You can't use binomial distribution.

anonymous · Answer

Never mind. I can't do this :( .