Question

ABC Company is planning on purchasing business interruption insurance from an insurance broker. The insurance broker examined the potential costs (in millions) and the likelihood of the following events, and estimated the expected annual cost of coverage to the company (insurance company) to be $1.25 million. However, due to a data file corruption, the broker lost some information, and is trying to recover it using the information remaining.

	Chance of Occurrence	Payout
No Interruption	?	0
Moderate Disruption	?	6.30
Full Disruption	0.05	14.14

Using this remaining information, what was the chance that ABC Company would experience a moderate disruption?

Answer 1

Let probability of ABC company would experience moderate disruption =x, then the chance of occurrence of no interruptions = (1-x-0.05).

I.e

chance of moderate disruption=x

chance of no interruptions=(1-x-0.05)

chance of full disruption= 0.05

Now,

expected annual cost of coverage to the company=1.25 million

i.e expectations of x =E(x)=1.25

(1-x-0.05)*0+x*6.30+0.05*14.14= 1.25

6.3*x= 1.25-0.05*14.14=0.543

x= 0.543/6.3≈0.08619

the chance that ABC Company would experience a moderate disruption= 0.08619

Ans→0.08619

thanks!

stay safe!