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 $165,000. 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?

Just about the same question here, just change the numbers

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To calculate the expectation for the drilling company, we need to multiply the possible outcomes by their respective probabilities and sum them up.

Let's first determine the probability of not hitting anything:

P(nothing) = 1 - P(oil) - P(gas)
P(nothing) = 1 - 1/40 - 1/20
P(nothing) = 1 - 1/40 - 2/40
P(nothing) = 1 - 3/40
P(nothing) = 37/40

Now, we can calculate the expectation:

Expectation = (P(oil) * Income(oil)) + (P(gas) * Income(gas)) + (P(nothing) * Income(nothing))

Income(oil) = $375,000
Income(gas) = $165,000
Income(nothing) = $0

Expectation = (1/40 * $375,000) + (1/20 * $165,000) + (37/40 * $0)
Expectation = $9,375 + $8,250 + $0
Expectation = $17,625

Therefore, the expectation for the drilling company is $17,625.

To determine the expectation for the drilling company, we need to calculate the expected income by multiplying each possible outcome (hitting oil, hitting gas, and hitting nothing) by their respective probabilities and summing them up.

Let's break down the calculations step by step:

1. Calculate the probability of hitting oil: 1/40.
2. Calculate the expected income if oil is hit: $375,000.
3. Multiply the probability of hitting oil by the expected income if oil is hit: (1/40) x $375,000 = $9,375.
This represents the expected income if oil is hit.

4. Calculate the probability of hitting gas: 1/20.
5. Calculate the expected income if gas is hit: $165,000.
6. Multiply the probability of hitting gas by the expected income if gas is hit: (1/20) x $165,000 = $8,250.
This represents the expected income if gas is hit.

7. Calculate the probability of hitting nothing: 1 - (probability of hitting oil + probability of hitting gas).
In this case, the probability of hitting nothing is: 1 - (1/40 + 1/20) = 1 - (1/40 + 2/40) = 1 - 3/40 = 37/40.

8. Calculate the expected income if nothing is hit: $0.
9. Multiply the probability of hitting nothing by the expected income if nothing is hit: (37/40) x $0 = $0.
This represents the expected income if nothing is hit.

10. Sum up the expected incomes: $9,375 + $8,250 + $0 = $17,625.

Therefore, the expectation for the drilling company is $17,625.