Expert: Surajit Basu - 4/4/2008

Question
You are the Chief Executive Officer (CEO) of IHI Insurance and last week one of your major policyholders lodged a large claim that could have devastating effects on the solvency of your company. You approach your Chief Financial Officer (CFO) who informs you that the probability of such a large claim being lodged is 0.6700. The CFO also states that the probability of making a profit and having such a large claim lodged is 0.1541.

Based on the information provided by the CFO, you conclude that the probability that IHI Insurance makes a profit this year, given that such a large claim has been lodged, is:

0.1541
0.1032
0.2300
4.3478

Answer
Let's solve a similar problem.

The chance that it will rain tomorrow where I stay is 0.25 ( once in 4 days).

The chance that it will rain tomorrow and my boss will yell at me is 0.1.


So, what is the chance that my boss will yell at me, if it rains tomorrow?

Suppose that it is P.


No, the chance that it will rain tomorrow and my boss will yell at me is  0.25 * P (both have to occur)

we now know that 0.25 * P = 0.1.
Thus, P is 0.1/0.25.


See:
http://en.wikipedia.org/wiki/Bayes'_theorem




Ok. So, now you can do your problem.

Try it



























The chance that (there'll be a large claim) is 0.67.

The chance that (there'll be a large claim) and (we'll make a profit) is 0.1541.


So, what is the chance that (we'll make a profit), if (there's a large claim)

Suppose that it is P.


No, the chance that (there'll be a large claim) and (we'll make a profit)is  0.67 * P (both have to occur)

we now know that 0.67 * P = 0.1541.


So, P is .....