Re: **** Probability Conundrum **** advice Please
Alan M. Zaslavsky (zaslavsk@hustat.harvard.edu)
Mon, 1 Aug 94 09:48:48 EDT
> Two prospects have been identified and will be drilled one after the other.
> They have colected/estimated the following data by evaluating the prospects
> *independently*.
> Cost of drilling PV of cash flows Prob. of Success
> if Successful
> Prospect A $10m $30m 0.32
> " B $10m $40m 0.32
>
> What they don't understand is how to deal with the geologist's comment that a
> successful first well would prove the presence of a source, and that this
> would alter the ex-post probability estimates of the 2nd prospect as follows:
> First Well Outcome Source Prob. Overall Prob.
> Success 0.8 0.512
> Failure 0.5 0.32
The probability assessments given in this problem are inconsistent. The
unconditional probability of success of Prospect A from the top line is
0.32. However, we can also use the information at the bottom to get
P(success at A)=P(success A | success B) * P(success B)
+ P(success A | failure B) * P(failure B)
= .512 * .32 + .32 * (1-.32)
> .32
The problem of course is that if finding out that (conditioning on) B
is successful increases the probability of success at A, then finding
out that B is dry must decrease the probability of success at A.