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 $415,000. If only natural gas is hit, the income will be $145,000. 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?
x: 400,000 , 100,000, -25000
Matched probabilities are (1/40) , 1/20, 37/40
Expected profit = (1/40)*400,000 + (2/40)100,000 - (35/40)(25000)
E(x) = [400,000+200,000-875000)/40
E(x) = -$6875
Hmm...
I would think
expected profit (oil)=415000-25000=390000
expected profit (gas)=145000-25000=120000
To calculate the expectation for the drilling company, we need to consider the potential outcomes and their associated probabilities, and then multiply each outcome by its corresponding probability.
Let's break down the potential outcomes and their probabilities:
1. Hitting oil (probability = 1/40)
- Income = $415,000
- Probability = 1/40
2. Hitting gas (probability = 1/20)
- Income = $145,000
- Probability = 1/20
3. Hitting nothing (probability = 1 - (1/40) - (1/20) = 37/40)
- Income = $0
- Probability = 37/40
Now, let's calculate the expectation:
Expectation = (income1 * probability1) + (income2 * probability2) + (income3 * probability3)
Expectation = ($415,000 * (1/40)) + ($145,000 * (1/20)) + ($0 * (37/40))
Simplifying:
Expectation = $10,375 + $7,250 + $0
Expectation = $17,625
Therefore, the expectation for the drilling company is $17,625.