For part B it should be .1*(85-10) + .9*(-10) = -1.5 billion.  If you obtain the patent your expected profit is 85 billion but you have  spent 10 billion to obtain the patent and so if you obtain the patent, your net profit is 75 billion.

Part B

I think "profit" implies costs have already been subtracted, so expected NPV is, as has already been argued:

.9 * -10 + .1 * 85 = -.5

I believe Waddle is correct.  The definition of profit implies inclusion of all costs.  -$.5 Billion would then be the correct.  The problem could have been written more clearly however. 

Ken

The -$10 Billion is already an average value.
So Part B is:
NPV = -10 Billion + (0.10)($85 Billion) = -1.5 Billion

CardinalEmpired on 6/26/06 is correct.

Dylan on 8/7/2007 is correct too with -1.5 Billion for Part B.
Dylan used:
For part B it should be .1*(85-10) + .9*(-10) = -1.5 billion. If you obtain the patent your expected profit is 85 billion but you have spent 10 billion to obtain the patent and so if you obtain the patent, your net profit is 75 billion.

Part E seems to have a typo -- change the million to billions.