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 $355,000. 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?
expectation = (1/40)(355000) + (1/20(130000)
= 15375
since it costs $25000 just to drill the well, this is not a good investment.
To find the expectation for the drilling company, we need to calculate the expected value for each possible outcome and then sum them up.
Let's break down the calculation step by step:
1. Expected income if oil is hit: Since the probability of hitting oil is 1/40, the expected income from hitting oil is (1/40) * $355,000 = $8,875.
2. Expected income if gas is hit: Since the probability of hitting gas is 1/20, the expected income from hitting gas is (1/20) * $130,000 = $6,500.
3. Expected income if nothing is hit: Since there's no income if nothing is hit, the expected income in this case is $0.
Now, we can calculate the expectation:
Probability 1: Hit oil = 1/40
Expected income from oil = $8,875
Probability 2: Hit gas = 1/20
Expected income from gas = $6,500
Probability 3: Hit neither = 1 - (1/40 + 1/20) = 37/40
Expected income from neither = $0
To calculate the expectation, we multiply each expected income with its respective probability and sum them up:
Expectation = (Probability 1 * Expected income from oil) + (Probability 2 * Expected income from gas) + (Probability 3 * Expected income from neither)
Expectation = (1/40 * $8,875) + (1/20 * $6,500) + (37/40 * $0)
Simplifying this, we get:
Expectation = $221.875 + $325 + $0
Therefore, the expectation for the drilling company is $546,875.