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 $425,000. If only natural gas is hit, the income will be $155,000. 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?

Please Don't spam, don't submit to many question at the same time in different post! We try are best to answer.

Thank You!
Unknown

http://www.jiskha.com/display.cgi?id=1363184716

To calculate the expectation for the drilling company, we need to multiply each possible outcome by its corresponding probability, and then sum up these values.

Let's define the outcomes and their probabilities:
- Outcome 1: Hitting oil, with a 1/40 probability (since there is a 1 in 40 chance of hitting oil).
- Outcome 2: Hitting gas, with a 1/20 probability (since there is a 1 in 20 chance of hitting gas).
- Outcome 3: Not hitting anything, with a probability of 1 - (1/40 + 1/20) = 37/40 (since the remaining probability is the chance of not hitting oil or gas).

Now, let's calculate the expectation:
Expected value = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2) + (Outcome 3 * Probability 3)

Expected value = ($425,000 * 1/40) + ($155,000 * 1/20) + ($0 * 37/40)

Simplifying the expression, we have:
Expected value = $10,625 + $7,750 + $0
Expected value = $18,375

Therefore, the expectation for the drilling company is $18,375.