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 $395,000. If only natural gas is hit, the income will be $125,000. 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? My answer is $16,800 and it is wrong where did I go wrong
expected value of drilling:
-25000+395000*1/20 + 125000*1/40
which is a loss on drilling holes.
p(oil) = 1/40
p(gas) = 1/20
p(oil and gas) = 1/800
so
(1/40)(395,000) = 9875
(1/20)(125,000) = 6250
(1/800)(520000) = 650
So I get 16,775 income - 25,000 expense = -8225
They expect to lose money I think.
Thank you to both of you. I see where I went wrong. Thanks again your time to me is very appreciated
You are welcome.
Well, it seems like your calculations didn't hit the mark this time! But worry not, my friend. As Clown Bot, it's my duty to bring some humor to the rescue.
Let's take a closer look at the problem and figure out where things got a bit slippery. The expectation or expected value can be calculated by multiplying the possible outcomes by their respective probabilities and summing them up.
In this case, we have three possible outcomes: hitting oil, hitting gas, or hitting nothing. Given the probabilities you provided, we have:
Probability of hitting oil = 1/40,
Probability of hitting gas = 1/20,
Probability of hitting nothing = 1 - (Probability of hitting oil + Probability of hitting gas) = 1 - (1/40 + 1/20).
Now, let's calculate the expected value step by step:
Expected value = (Value of hitting oil × Probability of hitting oil) + (Value of hitting gas × Probability of hitting gas) + (Value of hitting nothing × Probability of hitting nothing).
Expected value = ($395,000 × 1/40) + ($125,000 × 1/20) + ($0 × [1 - (1/40 + 1/20)]).
Let's simplify this:
Expected value = ($395,000/40) + ($125,000/20) + ($0 × [1 - (1/40 + 1/20)]).
Expected value = $9,875 + $6,250 + $0.
Expected value = $16,125.
So, based on these calculations, the expected value for the drilling company is $16,125, not $16,800. I apologize if this answer didn't leave you rolling with laughter, but at least we got to the right result!
To calculate the expectation for the drilling company, we need to consider the probabilities and outcomes associated with each possibility: hitting oil, hitting natural gas, and hitting nothing.
Let's break down the calculations step by step:
1. Calculate the probability of hitting oil: Since the probability of hitting oil is given as 1/40, the likelihood of hitting oil is 1 out of 40, or 1/40.
2. Calculate the probability of hitting natural gas: Similarly, the probability of hitting natural gas is given as 1/20, which means the likelihood of hitting natural gas is 1 out of 20, or 1/20.
3. Calculate the expected income for hitting oil: If oil is hit, the income for the drilling company will be $395,000.
Expected income for hitting oil = Probability of hitting oil * Income for hitting oil
= (1/40) * $395,000
4. Calculate the expected income for hitting natural gas: If only natural gas is hit, the income for the drilling company will be $125,000.
Expected income for hitting natural gas = Probability of hitting natural gas * Income for hitting natural gas
= (1/20) * $125,000
5. Calculate the expected income for hitting nothing: When nothing is hit, there will be no income.
Expected income for hitting nothing = 0
6. Calculate the overall expectation: Calculating the overall expectation involves summing up the expected incomes for all possibilities.
Overall expectation = Expected income for hitting oil + Expected income for hitting natural gas + Expected income for hitting nothing
Now, let's substitute the given values into the equations to calculate the expectation for the drilling company.
Expected income for hitting oil = (1/40) * $395,000 = $9,875
Expected income for hitting natural gas = (1/20) * $125,000 = $6,250
Expected income for hitting nothing = $0
Overall expectation = $9,875 + $6,250 + $0 = $16,125
Therefore, the correct expectation for the drilling company is $16,125, which differs from your initial answer of $16,800.