There are four grocery stores in your neighborhood and you are the manager of one of them. A customer has returned a relatively expensive and damaged item for a refund without a sales slip. You know that the item is carried by all four stores and you account for 65% of the sales of the item in the neighborhood. You are more careful in screening these items as you buy them, hence usually only have 0.25% defectives in your inventory. Your estimate of % defectives at your competitors is 0.3%.
What is the chance that the customer bought the item from you?
If you do not give a refund, your eventual loss of good will is $175 if the person did buy the item from you. The future earnings from this customer are $150 if you make the refund regardless of whether he bought it from you or not. There is no loss or gain if the item was not bought from you and you do not refund. The cost of the refund to you is $35. On a mathematical basis, should you make the refund?