Question

5. A company has 7 geophysical prospects in a certain area. From past experience it is estimated that 4 will prove to be dry, 2 will discover reserves of about 20 MM bbl, and one will discover reserves of about 80 MM bbl.
   1. What are the possible outcomes of the next 2 wells with one dry well and the discovery of one large reserve.
   2. Calculate the total reserves and expected value of this discovery. (only these information given in question)

Answer 1

a)

Dry p(D) = 4/7

Normal p(N) = 2/7

Large p(L) = 1/7

Poosible outcomes of next 2 wells will be out of (D,N,L) for both wells

Total possible outcome for 2 wells

1.D,D

2.D,N

3.D,L

4.N,D

5.N,N

6.N,L

7.L,D

8.L,N

9.L,L

b)

for above nine cases, lets find the reserves and the probability

1.D,D..... p=4/7*4/7.... reserves = 0 + 0

2.D,N..... p=4/7*2/7.... reserves = 0 + 20

3.D,L..... p=4/7*1/7.... reserves = 0 + 80

4.N,D..... p=2/7*4/7.... reserves = 20 + 0

5.N,N..... p=2/7*2/7.... reserves = 20 + 20

6.N,L..... p=2/7*1/7.... reserves = 20 + 80

7.L,D..... p=1/7*4/7.... reserves = 80 + 0

8.L,N..... p=1/7*2/7.... reserves = 80 + 20

9.L,L..... p=1/7*1/7.... reserves = 80 + 80

Expected value of discovery is sum of product of probabilities and respective reserves

Case	Probability	Reserve
1	0.3265	0
2	0.1633	20
3	0.0816	80
4	0.1633	20
5	0.0816	40
6	0.0408	100
7	0.0816	80
8	0.0408	100
9	0.0204	160

Expected value will be 34.29