An insurance company writes only automobile insurance. Depending on the
initial claim information received by the company, preliminary opening
reserves are established by the claims department in the following manner:
Type of Claim State A State B State C
Bodily Injury (serious) $5,000 $3,000 $2,000
Bodily Injury (not ser.) $1,000 $3,000 $2,000
Property Damage $1,000 $2,000 $1,000
According to the cmopany's statistics, 60% of claims are property damage, 30%
are non-serious BI, and 10% are serious BI. Also, the company's claims are
distributed 40% State A, 40% State B, and 20% State C.
Each claim file includes the details for only one of the three types of claim
every month; the claims manager does an audit of each examiner's files to
ensure that the initial reserves are properly set by pulling three files at
random--one for each type of loss.
What is the probability that the total dollars of reserves involved in any
examiners audit exceeds $7,500?
I set it up as follows:
S f(x1) f(x2) f(x3) f(x1x2) f(s)
$1000 0 .4 .6 0
$2000 .2 .2 .4 .08
$3000 .4 .4 0
$4000 0 0 0
$5000 .4 0 0
$6000 0 0 0
$7000 0 0 0
$8000 0 0 0
ETC.....Then I did 1- pr(s<7500) = 7.6%
Actex got .32; but I think they made a mistake.......HELP!!