F 100 tires are randomly selected for shipment to an outlet what is the probability that they are all good?

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.