# Thread: Find the least value of n

1. ## Find the least value of n

The question goes like this:

On average, out of every 1000 items made by a certain factory worker, 1 item is defective. The items are inspected in batches. A large number of batches, each of n items, made by the worker are inspected.. The probability of at least one defective item in a batch of n items is greater than 0.02. Find the least value of n.

I'm not sure how to begin. Is the no. of trails n or 1000 items?

2. ## Re: Find the least value of n

Originally Posted by pumbaa213
The question goes like this:

On average, out of every 1000 items made by a certain factory worker, 1 item is defective. The items are inspected in batches. A large number of batches, each of n items, made by the worker are inspected.. The probability of at least one defective item in a batch of n items is greater than 0.02. Find the least value of n.

I'm not sure how to begin. Is the no. of trails n or 1000 items?

the probability of that worker making a defective item is p=1/1000

The probability of finding at least 1 defective item out of a batch N is

$1 - (1-p)^N > 0.02$

$(1-p)^N < 0.98$

$N\log(1-0.001) < \log(0.98)$ ; note the inequality flips because the log is negative

$N = \frac{\log(0.98)}{\log(0.999)} > 20.19 \Rightarrow N>21$

3. ## Re: Find the least value of n

haha (once again)thanks romsek! You've been a great help to me and my homework!