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Is there a word or phrase for cost due to risk. For example, if my $1.000 car has a chance of breaking of 1% per ride, the cost due to risk would be $10 per ride.
Example sentence:
While driving to France, the [word here] was split evenly between the passengers.
A mathematician calls such values expected value or expectation or mean value or average: the probability of an event happening (here: 0.01) times the value of the random variable of interest if the event occurs (here: $1000), assuming that the random variable is zero when the named event doesn't occur. What we talk about here is a possible loss, so the complete phrase would be expected loss (or: expected loss with respect to the possibility of a breakdown).
However, this would sound completely misleading in your sentence in everyday speech because instead of $10 expected loss, a layperson would expect zero loss, except when the unlikely happens.
What would be somewhat better and still scientifically correct is average loss.
But your sentence itself is odd. If passengers split that amount that way, it means that they arrange themselves into an insurance policyholder, where the car owner spontaneously becomes an insurer (cf. @Bilkokuya).
I do not believe there is a word that will fit your sentence as it is structured, and be clearly understandable.
However, the idea you are talking about (sharing the cost of a potential risk), is a form of insurance
Insurance is a means of protection from financial loss. It is a form of risk management primarily used to hedge against the risk of a contingent, uncertain loss.
With their payments being insurance premiums.
Premium is an amount paid periodically to the insurer by the insured for covering his risk.
That is, your friends are paying a small insurance premium, to cover the cost of your car against the potential risk of damage.
This said, insurance will tend to suggest that you are paying a small amount to a large company - on the basis that they cover the entire cost of repair if something does go wrong. I don't feel you can communicate the exact arrangement clearly - without including the details of it:
Each passenger paid an insurance premium of $10 to cover the potential risks to the car.
indemnity TFD
indemnity is an obligation by a person (indemnitor) to provide compensation for a particular loss suffered by another person (indemnitee); security against damage, loss, or injury.
AS in:
While driving to France, the indemnity was split evenly between the passengers.
versus cost of trip ie gas, tolls, etc
