1. A company operates 80 wells in an area of Texas. Fifty of the wells have dept
ID: 3310819 • Letter: 1
Question
1. A company operates 80 wells in an area of Texas. Fifty of the wells have depth less than 10,000 feet and are considered as Shallow wells. The remaining 30 wells reached depths greater than 10,000 feet and considered as deep wells. From shallow wells, 15 produce oil and 35 produce gas. On the other hand, 6 deep wells produce oil and the rest produce gas. a) What is the probability that a well is shallow? What about deep? b) What is the probability that a well is a gas well? What about oil? c) Knowing that a well is shallow, what is the probability of having an oil producer? d) What is the probability that a well is shallow and oil? e) Known that a well needs to be repaired, what is the probability that it will be a deep well? 2. An exam consists of 10 four-option multiple choice questions. If you answer the questions totally by guessing, 1) What is the probability of getting exactly 6 right answers? 2) What is the probability of getting more than 8 right answers? 3) What is the expected number of right answers? 4) Please tabulate and plot the probability mass function.Explanation / Answer
(1)
Given that,
Total wells n =80
Shallow wells n(S) =50
Deep wells n(D) = 30
Oil wells n(O) = 21
Gas wells n(G) = 59
Shallow oil wells n(O|S) =15
Deep oil wells n(O|D) = 6
Shallow gas wells n(G|S) =35
Deep gas wells n(G|D) = 24
We know that, Probability P= m/n
where, m is favourable events and n is total events
a)
Probability of shallow wells P(S) = 50/80 = 5/8 = 0.625
Probability of deep wells P(D) = 30/80 = 3/8 = 0.375
b)
Probability of gas wells P(G) = 59/80 = 0.7375
Probability of oil wells P(O) = 21/80 = 0.2625
c)
Knowing that a well is shallow,
Probability of oil wells P(O) = 15/50 = 0.3
d)
Probability of a shallow oil wells P(O) = (15*50)/[(15*50)+(6*30)] = 0.8065
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