Question

Based on historical data, an insurance company estimates that a particular customer has a 2.4% likelihood of having an accident in the next year, with the average insurance payout being $2700.


If the company charges this customer an annual premium of $250, what is the company's expected value of this insurance policy?

Answer 1

Answer:

The expected value of this insurance policy is kept at $185.2 based on the historical data provided

Step-by-step explanation:

probability/likelihood of having an accident by the customer is = 2.4% which is 2.4÷100 = 0.024 probability :

The cost to the company at 0.024 probability of having an accident

=  - $2700 (average insurance payout)

probability of not having an accident by the customer is =  100% - 2.4%  = 97.6% which is 97.6 ÷ 100 = 0.976 probability

The cost to the company at 0.976 probability of no accident = $0

The premium paid by the customer annually is = $250

Therefore to get the expected value of the insurance policy (E) will be

(probability of accident) (average insurance payout) + (probability of no accident) (cost of no accident to the company) + premium paid by customer  

0.024(-$2700) + 0.976($0) + $250 = $185.2

- $64.8 + $0 + $250 = $185.2

Answer 2

The company's expected value of this insurance policy is 185.2.

What is the expected value?

The expected value formula is the product of the probability of the product of an event and the number of times the event happens.

$E(x)= \sum( P\times n)$

As it is given that the likelihood of a particular customer paying $250 for the insurance is 2.4%(0.024). And, if the customer faces an accident then the average insurance payout is $2700, therefore, the average insurance payout is -$2700.

Now, the chances of the customer not facing an accident are 97.6% because the sum of all the probability is 1.

Probability of facing an accident + Probability of not facing an accident = 1

0.024 + Probability of not facing an accident = 1

Probability of not facing an accident = 1 - 0.024

Probability of not facing an accident = 0.976

And, the average insurance payout is $0, when the customer not facing an accident.

Now, the company's expected value of this insurance policy can be written as,

(Probability of accident × Average insurance payout) + (Probability of no accident × cost of no accident to the company) + Premium paid by the customer

$E(x)= (0.024 \times -2700)+(0.976 \times0)+250$

        $=(0.024 \times -2700)+(0.976 \times0)+250\\\\=-64.8+0+250\\\\=185.2$

Hence, the company's expected value of this insurance policy is 185.2.

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