Solving Probability Problem: Finding a Well of Water at a Depth of <100ft

In summary, the conversation discusses the probability of finding a well of water at a depth less than 100 feet in a certain area. It mentions that the probability is 0.6 for each drilling and that this event is independent from drilling to drilling. The conversation then presents different questions related to this probability, including finding the probability of a certain number of wells being found, calculating the mean and variance, and determining the probability of a specific number of wells being found.
  • #1
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Hi,
I need have this problem check because I have a problem at the last question:

the probability is 0.6 that a well driller will find a well of water at a depth less than 100 feet in a certain area. Wells are to be drilled for six new homeowners. Assue that finding a well of water at a depth of less than 100 feet is independent from drilling to drilling and that the probability is 0.6 on every drilling. If X is the number of wells of water found. Find:

1-P(X>4)
My solution: P(X>4)=1-B(4;6,0.6)

2-P(X=4)
P(X=4)=b(4;6,0.6)

3-mean
mean=n*p=3.6

4-variance
Var^2=n*p*(1-p)=1.44

5-P(X=mean)
Here since mean =3.6, I have problem to find P(X=mean)

Thank you
B.
 
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  • #2
brad sue said:
Hi,
I need have this problem check because I have a problem at the last question:

the probability is 0.6 that a well driller will find a well of water at a depth less than 100 feet in a certain area. Wells are to be drilled for six new homeowners. Assue that finding a well of water at a depth of less than 100 feet is independent from drilling to drilling and that the probability is 0.6 on every drilling. If X is the number of wells of water found. Find:

1-P(X>4)
My solution: P(X>4)=1-B(4;6,0.6)
B is the binomial probability? Isn't B(4;6,0.6) the probability of exactly 4 "sucesses" out of 6? If so 1- B(4;6,0,6) is P(X= 1, 2, 3, 5, or 6). What you want is P(5;6,0.6)+ P(6;6,0.6).

2-P(X=4)
P(X=4)=b(4;6,0.6)
?? Is "b" different from "B"? If not then what I thought above was true. This is correct, 1 is incorrect. Oh, and have you actually calculated that value?

3-mean
mean=n*p=3.6

4-variance
Var^2=n*p*(1-p)=1.44
Okay.

5-P(X=mean)
Here since mean =3.6, I have problem to find P(X=mean)

Thank you
B.
Well, that last one is kind of trivial isn't it!
 
  • #3
But my calculator does not give me a approximate value for b(3.6;4,0.6) ! ( for question 5)
 
  • #4
You are supposed to be smarter than your calculuator! Stop and THINK. If you drill 6 wells, each well either will or won't hit water, what is the probability that exactly 3.6 of them will hit water?!
 
  • #5
HallsofIvy said:
You are supposed to be smarter than your calculuator! Stop and THINK. If you drill 6 wells, each well either will or won't hit water, what is the probability that exactly 3.6 of them will hit water?!

Each well has a probability of 0.5 to hit water. So the probability of exactly 3.6 wells each 0.5^3.6= 0.082 ??
 

1. How do you calculate the probability of finding a well of water at a depth of less than 100ft?

The probability of finding a well of water at a depth of less than 100ft can be calculated by dividing the number of successful outcomes (finding a well) by the total number of possible outcomes (all depths less than 100ft). This can be expressed as a fraction or decimal and multiplied by 100 to get a percentage.

2. What factors affect the probability of finding a well of water at a depth of less than 100ft?

Several factors can affect the probability of finding a well of water at a depth of less than 100ft, such as geological conditions, proximity to water sources, and drilling techniques. Additionally, the availability and quality of data and the expertise of the survey team can also influence the probability.

3. How can a probability problem be solved using statistical methods?

To solve a probability problem using statistical methods, data can be collected from previous well-drilling projects in similar areas and analyzed using various statistical tools and techniques. This can provide insights into the likelihood of finding a well at a specific depth and can help in making informed decisions.

4. Is it possible to accurately predict the probability of finding a well of water at a depth of less than 100ft?

While statistical methods can provide an estimate of the probability, it is important to keep in mind that there are many variables involved in drilling for water and the accuracy of predictions may vary. Factors such as unforeseen geological conditions and human error can affect the actual outcome.

5. How can one increase the probability of finding a well of water at a depth of less than 100ft?

To increase the probability of finding a well of water at a depth of less than 100ft, it is important to conduct thorough research and gather as much data as possible before beginning the drilling process. This can help in identifying the most promising locations and optimizing drilling techniques. Seeking the expertise of experienced professionals can also improve the chances of success.

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