Lets calculate an example:
Say, .001% of tires that come from the factory are bad. There is a 1/1000 chance that for any given tire randomly selected from the warehouse that a defect will be present. Each tire is a mutually exclusive independently occurring event in this case. The probability that a single tire will be good or bad, does not depend on how many tires are shipped in proportion to this known .001% (or 1/1000) defect rate.
To get the probability in a case like this, that all tires are good in a shipment of 100, with a factory defect rate of .001%, first divide 999/1000. We know that .999% of tires are good. Since 1/1000 is bad, 999/1000 are good. Now, multiply .999 x .999 x .999..etc until you account for every tire in the group of 100 shipped. (.999 to the hundredth power)
This gives us 0.90479214711 which rounds to about .90. or a 90% probability.
So for this example, in a shipment of 100 tires, with a .001% factory defect rate, the probability is about 90 percent that all tires will be good.
Remember, the tires are mutually exclusive and independent of each other when using something like a factory defect rate to calculate the probability that a shipment will be good.
