Consider the well failure data in Exercise 2-53. Let A

Chapter 2, Problem 77E

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QUESTION:

Consider the well failure data in Exercise 2-53. Let denote the event that the geological formation has more than 1000 wells, and let  denote the event that a well failed. Determine

the following probabilities.

(a) \(P(A \cap B)\)         (b) \(P\left(A^{\prime}\right)\)         (c) \(P(A \cup B)\)        (d) \(P\left(A \cup B^{\prime}\right)\)         (e) \(P\left(A^{\prime} \cap B^{\prime}\right)\)

Equation transcription:

Text transcription:

P(A cap B)

P(A^{prime})

P(A cup B)

P\left(A cup B^{prime})

P\left(A^{prime} cap B^{prime})

Questions & Answers

QUESTION:

Consider the well failure data in Exercise 2-53. Let denote the event that the geological formation has more than 1000 wells, and let  denote the event that a well failed. Determine

the following probabilities.

(a) \(P(A \cap B)\)         (b) \(P\left(A^{\prime}\right)\)         (c) \(P(A \cup B)\)        (d) \(P\left(A \cup B^{\prime}\right)\)         (e) \(P\left(A^{\prime} \cap B^{\prime}\right)\)

Equation transcription:

Text transcription:

P(A cap B)

P(A^{prime})

P(A cup B)

P\left(A cup B^{prime})

P\left(A^{prime} cap B^{prime})

ANSWER:

Solution:

Step 1 of 6:

The data regarding the geographical formation, total number of wells and number of failed wells are given.

Geographical formation group

                                      Wells

Failed

Total

Gneiss

170

1685

Granite

2

28

Loch raven schist

443

3733

Mafic

14

363

Marble

29

309

Prettyboy schist

60

1403

Other schists

46

933

Serpentined

3

39

Also, it is given that A denotes the event that the geographical location has more than 1000 wells and B denotes the event that a well failed.

Using this we need to find the required values.


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