# What are the probabilities involved with package shipping insurance?

## Main Question or Discussion Point

The situation is, I purchase an insurance for loss of a package during shipment, the insurance fee is 0.5% of the claimed actual value of the package, but this is optional, you don't need to purchase insurance but you will not get compensated if the package is lost.. Assume that the shipping company is not intended to earn money through the insurance, and they only use the insurance fee collected to pay for the loss of the package of other customers. What is the probability of losing a package? Is it also not higher than 0.5% ? Is it that simple?

## Answers and Replies

PeroK
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Homework Helper
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The situation is, I purchase an insurance for loss of a package during shipment, the insurance fee is 0.5% of the claimed actual value of the package, but this is optional, you don't need to purchase insurance but you will not get compensated if the package is lost.. Assume that the shipping company is not intended to earn money through the insurance, and they only use the insurance fee collected to pay for the loss of the package of other customers. What is the probability of losing a package? Is it also not higher than 0.5% ? Is it that simple?
Essentially, yes it's a simple equation. If they have 200 customers and each pay 0.5%, then the company gets enough in insurance to pay for one additional product. So, if 1 out of the 200 items goes missing, then the total insurance money collected pays for the replacement.

You could, of course, make other assumptions. Most obviously, the cost of replacement to the company is not the full price the customer pays. It may only be 50%, say. If you buy a product for $500, then it may only cost a company$250 to replace it.

In that case, the insurance fee of 0.5% would cover a loss of 1 out of every 100 shipments.

Essentially, yes it's a simple equation. If they have 200 customers and each pay 0.5%, then the company gets enough in insurance to pay for one additional product. So, if 1 out of the 200 items goes missing, then the total insurance money collected pays for the replacement.

You could, of course, make other assumptions. Most obviously, the cost of replacement to the company is not the full price the customer pays. It may only be 50%, say. If you buy a product for $500, then it may only cost a company$250 to replace it.

In that case, the insurance fee of 0.5% would cover a loss of 1 out of every 100 shipments.
Hi, in real life every day situation, if I often ship package, is it better NOT to purchase such insurance
because the insurance fee I've paid will probably more than what I'll lose in a rare case that the package
gets lost? Like the expected value of casino?

And if I only ship package sometimes, not very often, then it's just a matter of probability and it really
shouldn't make much difference whether I purchase such insurance ?

Am I understanding correctly??

PeroK
Science Advisor
Homework Helper
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Whether you insure something is your decision. In general,insuring against small losses may not be cost effective.

phinds
Science Advisor
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2019 Award
I've shipped well over 1,000 boxes over the last 15 years (all via USPS). Never insured any, never had any lost. Had one arrive 28 days late due to Katrina but that was the worse case. Had I insured them I'd be out about \$2,500

PeroK