Calculating Probability and Profit for Drilling Wells: A Binomial Approach

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The discussion focuses on calculating the probability distribution and expected net profit for drilling 5 exploratory wells, with varying probabilities of discovery based on earlier outcomes. The probability of a discovery in the first three wells is set at 0.20, with subsequent probabilities of 0.40 or 0.15 depending on the initial results. Participants clarify that a discovery in the first three wells likely means at least one successful well, and confirm that the profit function is indeed $3,000,000 times the number of discoveries minus the total drilling costs. There are concerns about discrepancies in expected standard deviation and net profit calculations, with some participants noting the potential for negative profits. The conversation emphasizes the complexity of applying binomial probabilities in this scenario.
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QUESTION3:
Alexander Da Costa & Priyanka Kapadia Petroleum, plans to drill 5 exploratory wells. Jenny Wong & Danny Tieu Consulting geologists give the probability that a well results in a discovery as 0.20 for the first 3 wells. If there is a discovery in the first 3 wells the geologist's probability is 0.40 for the next 2 wells. Otherwise the geologists give a probability of 0.15 for the next 2 wells. Digging each well cost $500,000, and each successful well will result in a profit of $3,000,000 (before subtracting cost of digging the well),

a. Use binomial probabilities and a tree diagram to find the probability distribution of the number of discoveries.
b. What will be the expected net profit and the standard deviation?
c. Does the distribution in part a) agree with the binomial distribution for n=5, and p=0.20? Why? Why not?

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I have a few issues. When they say, If there is a discovery in the first 3 wells, does that mean 1 discovery in any of the first 3 wells, or discovery in all 3 of the first 3 wells.

Also, would the profit function be 3000000x - 2500000?

Help is greatly appreciatd
 
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cant anyone help me?
 
wont anyone help me?
 
Probably it means at least 1 discovery out of all 3 wells. Yes, that would be the profit function.
 
i tried it that way and somewhere i am making a mistake...my expected standard deviation is MUCH MUCH higher than my expected net profit. But i guess it might be alright since there is a chance of negative profits
 

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