The unfortunately-named (and fictitious) town of Avalanche, Utah maintains a vibrant and growing ski industry.  As Director of Avalanche's search-and-rescue operations, you are always interested in the latest technologies that can help you find skiers and others who find misfortune.  Most recently, you have been exploring the use of a Snow Sonogram Machine (SSM), which allows you to scan very deep sections of snow for evidence of buried bodies.

The SSM is a good, but not perfect, machine.  If someone is buried in a pile of snow, the SSM will correctly identify the presence of person in that pile 90% of the time.  If someone is buried, the SSM will say that the buried person is not actually there 10% of the time.  If someone is not buried, the SSM will correctly say that there is no one buried 70% of the time, but incorrectly say that there is someone buried 30% of the time.

Sure enough, after a recent small avalanche, a girl has gone missing, and you suspect she might be buried in a small section of one nearby mountain.  Specifically, there is a 90% chance she is buried and 10% chance she is not.

Assume that if she is buried, the only way you can find her is to dig, and assume that you will definitely find her if you dig.  If she is not buried and you dig, you have no chance of finding her.  If she is not buried and you choose not to dig (that is, you put your resources towards other search processes), you have a 10% chance of finding her.

For simplicity's sake, assume that - if you find her - you find her alive.    

Now, estimating costs and benefits can be a tricky and emotional business when talking about human lives, but you do live in the real world of limited resources and accountability.  As such, you rely on the significant body of literature on the value of human lives, which estimates the value of finding the girl at $10 million.  If you do not find her, the benefit is $0. 

The other relevant costs and benefits are as follows:

• If you choose to use the SSM on the relevant section of mountain, you can rent it for $100,000
• Digging in the section of mountain (regardless of whether the SSM is used) costs $150,000
• Not digging (again, regardless of whether the SSM is used) costs $50,000, since you will engage in other, but less costly, search processes