Gotta agree with Nelson - the maths / statistics we are talking about here are not about straight averages / probability but more akin to bookies odds, and we all know who the overall winner is between the bookies and the punter!!!! The odds are stacked in favour of the insurance company winning, otherwise why would they offer the business in the first place - this ain't about break even, this is about shareholder value.
The fact is that your legally required to have a valid insurance policy in force - legislated by government - but the risk factors and premiums charged by the insurance companies are not legislated for, therefore, apart from competition in the market place (i.e read Cartel) it's a licence to print money.
On another point I've been involved with issuing car tax for years now and I'd say that 5-10% of all insurance documents that are presented are incorrect - be that incorrect name on policy, incorrect registration etc - all mistakes by the insurance companies, but technically with a mistake on the policy it's invalid and will be refused when applying for car tax. All these people have never noticed the mistake until it's pointed out to them, and you can bet if they claimed it would be a valid reason for the insurance companies to wriggle out of paying as it's your responsibility to check your policy when you receive it.