Exercise i can't solve

[paveer]

Hello;

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....

 

[katxt]

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"?

 

[paveer]

it's more the last one: any particular bottle has a probability of 300/5000 or 0.06 of being infected

 

[katxt]

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 ...

 

[paveer]

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?

 

[Dason]

Logarithms