Probabilities

Question

When company X ships a dozen eggs, there is a 3% chance that exactly one egg will be broken, a 0.5% chance that the whole dozen will be broken, but no chance that any other number of eggs will be broken. If 1,000 dozen eggs are ordered from company X, how many broken eggs should be expected?

Answer 1

First you find the number of eggs that are expected to be broken each time they ship a dozen eggs. 

 

- (3% * 1) + (.5%* 12) + (96.5% *0)

 

Make sure the probabilities add up to one. There is a 3% chance that one egg will break, a .5% chance 12 will break and 96.5% chance that no eggs will break at all. 

 

= (.03* 1) + (.005 *12) = .09 

 

Thus .09 eggs are expected to be broken for each batch of one dozen eggs. 

 

Second Step

 

If they are shipping 1000 dozen eggs, then we should expect that (.09 *1000) of the eggs should arrive broken. Since .09 eggs are expected to be broken for each dozen. 

 

Therefore 90 eggs will be broken.