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twesterm on 26 December 2008
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TheLivingShadow said:
twesterm said:

Fine, how about some simple statistic problems?

A trainload of unnamed consoles are set to arrive at a distribution center between 8 and 8:10PM. It is now 8:03PM and the train still has not arrived. Assuming the train will arrive in the designated window, what is the probability it will arrive within the next minute? What if it's 8:07PM and the train has still not arrived, what is the probability it will arrive within the next minute?

Say the same unnamed console has a failure rate of 1/10 within the first 15 minutes of being powered on. If there is a stack of 20 of these consoles and 8 have already been picked, tested for 15 minutes, and passes, what is the chance the one you pick will fail within the 15 minutes of being powered on?

Damn it I haven't had statistic classes yet, that's for next year's class. I'll try to figure out the answer though with reasoning rather than formulas because I do not know any of them.

Well, since the possibilities for the first question are 8:04, 8:05...8:10, there are 7 possibilities. then 7->100%. Since 8:04 represents one single possibility, then there is a probability of 14,29% for the train to arrive at 8:04.

For the second question, there are 3 possibilities, that it'll arrive at 8:08, 8:09 or 8:10. Then 3->100%. Since 8:08 represents one single possibility, then there is a probability of 33,33% for the train to arrive at 8:08.

For the last problem, since there's a failure rate of 10% for 20 consoles, then 2 of these consoles will fail. Since 8 have been already picked, that leaves us with 12 consoles, out of which 10 work and 2 fail. Now, 20->100% 2->10% of 20. And 12->60% of 20. 8->40% of 20.
Then we have 2->16,67% of 12. That's the chance we're looking for.

 That's it I hope I'm right. Why don't you try solving my problem twesterm? from the looks of your problems you're really smart.

I encourage everyone to continue answering problems and posting further problems!

 

First one, it's right but much easier to say 1/7 and 1/3. 

Second one is wrong.

Answer if you want to know but I'll keep it blacked out in case people want to think about it:

The answer is 1/10.  Every console has a 1/10 failure rate.  Just because 8 of those consoles haven't failed doesn't mean one of the next two will fail, they still have the same 1/10 chance of failing.  It's like if you flip a coin and it lands heads, it still has the same 1/2 chance to land on heads again if you flip it again.

Your answer would be correct if I said I had 20 marbles with 2 red ones and 18 black ones.  If 8 black ones had been picked, what is the chance I pick a red one?  1/6.