Exercise i can't solve


who can help me with the following exercise

"A company has produced 5000 bottles, they suspect that 300 bottles are infected.
Therefore inspection is required: if they find one infected bottle, the full set of 5000 bottles will be destroyed.

question: how many bottles do they need to inspect in order to achieve 99% probability of finding one infected bottle?"

I don't have any idea how to solve this....


Active Member
This is a rather oddly framed question. Do they mean "exactly 300/5000 bottles are infected" or "any particular bottle has a probability of 300/5000 or 0.06 of being infected"?


Active Member
So I guess the question boils down to "how many can you take and have the chance of all negatives = 0.01"
The chance of any one choice negative is 1 - 0.06 = 0.94
so the chance of getting k negatives in a row is 0.94^k = 0.01 Does that sound right? Over to you ...
you are completely right, answer was 75 bottles. Is there easy way to solve that equation?
in the course tables are provided for Bernoulli, can this be used?