It looks to me like an expected value problem.

In the scenario with no precaution the expected value is the chance of the contingency occurring, times the expected value if it does occur, so .9*(1*100,000)=90,000.

Precaution A gives an expected value of 50,000+(.9*(.3*100,000))=77,000

Precuation B gives an expected value of 75,000+(.9*(.1*100,000))=84,000

Since the scenario with the lowest expected value is Precaution A, I would allow the contractor to price the contingency at a maximum of $77,000.

Winner!

But wait. If the contractor did not price Precaution A or B into its FFP, then those hypothetical precautions are meaningless. Under Precaution A, you should allow $77,000 + $50,000 = $127,000. You need to allow the contractor to price in the cost of risk mitigation.

The total of $77k includes the $50k to pay for Precaution A, plus the expected value of the contingency, which is $27k (90% x 30% x $100k). It is interesting that there is no single scenario in which the contractor will actually experience a cost of $77k. Either they will pay the $50k for precaution A and then contingency either won't occur, or will cost $0, in which case their total cost will be only $50k, or they will pay the $50k and have bad luck anyway and still experience the $100k contingency, in which case their cost is $150k. Only if they run the scenario multiple times will they all average out to $77k in the long run.

Have any of ye land lubbers had experience using this method? Would a contractor actually be willin' to accept eatin' the $73k doubloons in Scenario A and $91k in Scenario B?  I may be cynical due to me sole-source encounters with dodgy contractors.

5 hours ago, Contracting Pirate said:

Have any of ye land lubbers had experience using this method? Would a contractor actually be willin' to accept eatin' the $73k doubloons in Scenario A and $91k in Scenario B?  I may be cynical due to me sole-source encounters with dodgy contractors.

The contractor doesn't have to eat the loss. They could buy insurance, right? 

On 12/4/2018 at 6:44 PM, Don Mansfield said:

Winner!

From the seller's perspective, at a 90% probability, I'd consider it a sure thing and price it assuming 100% of the costs would be incurred.

21 hours ago, lotus said:

From the seller's perspective, at a 90% probability, I'd consider it a sure thing and price it assuming 100% of the costs would be incurred.

That's exactly what the seller did in the problem.