Question

An oil-drilling company knows that it costs $25,000 to sink a test well. If oil is hit, the income for the drilling company will be $375,000. If only natural gas is hit, the income will be $130,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company

Answer 1

Expectation
= ΣxP(x)
where x represents the gain from each of the outcomes in the sample space.

Here the gains and probabilities are:

outcome=oil
gain=375000-25000=350000
P(oil)=1/40
xP(oil)=8750

outcome:gas
gain=130000-25000=105000
P(gas)=1/20
xP(gas)=5250

outcome:nothing
gain=0-25000=-25000
P(nothing)=1-1/40-1/20=37/40
xP(nothing)=-23125

Expected gain
E(x)=8750+5250-23125=-9125
(negative gain = loss)