AuthorTopic: need some help on a statistics challenge
nisarparas
@2018-06-22 09:06:42
I have a machine with only 2 outcomes:

A) success
B) failure

You only want to buy the machine if you have "reasonable assurance" that the machine can find success at least 1.0% of the time.

You run the machine through 10,000 trials and find that it has 120 successes, or a 1.2% success rate. Of course it’s possible this is a fluke. Can we be confident the machine meets the required specs? (allow the typical 5% window for a type II error)
ezeus2
@2018-06-22 11:08:21
So, what’s the probability of 120 successes if the actual success rate is 1.0%?
nisarparas
@2018-06-23 06:10:51
No, the question i'm trying to ask is,

What is the probability that this 120 success correctly indicates a minimum success rate of +1.0%?
ezeus2
@2018-06-23 15:29:17
I understand the question you’'re asking.

I asked a question that will lead you to the correct answer, and is one that you should be able to answer easily.

So, once again, what’s the probability of 120 successes if the actual success rate is 1.0%?
nisarparas
@2019-07-06 11:42:41
Gosh, I'm really struggling with this one. Let me try simplifying the problem here to a coin problem where the expected probability is 50%

If I had 5 coins and you asked about my chances of getting 3 heads, then my strategy would be 2^5 = 32 outcomes

(5*4*3) / (3*2*1) = 10 outcomes with order not mattering, giving me a 5/16 probability of hitting exactly 3 heads.

Am I on the right track here?