Question

A Vespa rental company charges a $200 premium for an insurance policy on a rental. If the Vespa is totaled, the insurance policy will cover the full cost of replacing the Vespa, $5000. For minor damage, the policy will cover $1000 in repair costs. The probability of the Vespa getting totaled is 0.004, while the probability that it will sustain minor damage is 0.1. What is the expected value of the policy for the company?

Answer 1

probability of totaled and paying $5000 is 0.004, probability of sustaining minor damage $1000 is 0.1 and total charge premium is $200

probability of neither totaled nor minor damage = 1- P(totaled)-P(minor damage)

= 1- 0.004 -0.1

= 0.896

x	P(x)
-$200	0.896
$5000	0.004
$1000	0.1

Expected value = Sum of all (x*P(X))

using the data table

= (-200*0.896)+(5000*0.004)+(1000*0.1)

= -179.2 + 20 + 100

= -$59.2

Expected value is net loss of $59.2