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## 'To Insure or Not to Insure' printed from http://nrich.maths.org/

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"Wow, great new phone!  How much did that set you back?"
"Don't ask - mega bucks!  Do you know what it can do ..."

1 month later ...

"I've just got a new phone!  Bet yours can't do what mine can!"
"I haven't got mine any more.  I lost it ... actually, I think it got stolen."
"But you had insurance, didn't you?"
"No, I didn't think it was worth it."
"Mine's insured - I wouldn't want to lose it!"
"But how much did that set you back?"
"Enough, but at least I don't have to worry about losing my phone!"

Who's right?  What are the issues?

Tom's new phone cost him £500.  He didn't insure it.
Alice's new phone cost her £500 also.  She did insure it, at an additional cost of £75.

Investigate the consequences for Tom and Alice if:

• there is a 10% chance of losing their phone (by any means)
• taking out insurance means that the phone is replaced on a like for like basis, whatever the cause of the loss
What would you do?

Do a survey around the class - how many people would insure, how many wouldn't?
What difference would it make if the probability of losing the phone is greater or smaller?

What are the consequences for the insurance company if:
• the chance a person loses their phone is 10% - that means that they can expect 1 in 10 people to lose their phones
• the phone is replaced on a like for like basis
• 20% of people take out insurance
What difference does it make if the 10% risk of losing a phone is 1% or 25%?
What difference does it make if the 50% of people taking out insurance is 10% or 75%?
See if you can find break-even points for the company.
You may find it helpful to consider a population of, say, 10,000.