Answer:
The expected loss for the car owner per year is $750.
Step-by-step explanation:
We are given that a car owner who has an 80% chance of no accidents in a year, a 20% chance of being in a single accident in a year, and no chance of being in more than one accident in a year.
Let X = Loss for the particular year for a car owner
Now as we know that the loss to the car owner may be of $0, $500, $5,000 or $15,000 because these amount he has to pay as a part of repair cost if his car met with an accident.
So, the probability distribution of X is given by;
X (Amount of Loss) P(X)
$0 0.80
$500 (0.20)(0.50) = 0.10
$5,000 (0.20)(0.40) = 0.08
$15,000 <u> (0.20)(0.10) = 0.02 </u>
Total <u> 1 </u>
Here, the probability of (0.20)(0.50) means that for the loss of $500, first the car must have to met with an accident and then there is 50% chance that after the accident the car will need repairs costing $500.
Now, the expected loss for the car owner per year is =
=
= 50 + 400 + 300 = $750.
So, the expected loss for the car owner per year is $750.