Re: simple stats problem
- From: quasi <quasi@xxxxxxxx>
- Date: Sun, 16 Mar 2008 01:39:08 -0500
On Sat, 15 Mar 2008 22:45:43 -0700 (PDT), Digital Puer
<digital_puer@xxxxxxxxxxx> wrote:
Hi, I've been trying to figure out this problem I got on an interview,
but I haven't been able to get a clear answer.
Suppose I have a room of N computers. Suppose each computer
fails at a rate of once every 14 days.
Now what is the probably that at least one of them fails?
I'm thinking it's 1 - prob(none of them fail). But then how do I
figure that out?
And if the question is what is the probably that at least one of them
fails, does that necessarily mean "out of those 14 days"? I didn't
have any other info than that.
Thanks for any help.
My guess is they want the probability of at least one failure for a
single day.
Assuming that the failure potential is "memoryless" (in other words,
the probability of failure for each computer is 1/14 on any given day,
regardless of the history of prior failures, and assuming the
computers are independent of each other with regard to failures, then
the probability of that no computer fails on a given day is (13/14)^N,
and hence the probability of at least one failure is 1 - (13/14)^N.
If you did want to consider 14 straight days, it's just as easy. The
probability of no failure for all computers for 14 straight days would
just be ((13/14)^N)^14 which simplifies to (13/14)^(14N). Hence the
probability that at least one of the N computers fails in 14 straight
days is 1 - ((13/14)^(14N)).
quasi
.
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