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amilapsn
 one year ago
An explosion at a construction site could have occurred as the result of static electricity, malfunctioning of equipment, carelessness or sabotage. Interviews with construction engineers analysing the risks involved led to the estimates that such an explosion would occur with probability 0.25 as a result of static electricity, 0.20 as a result of malfunctioning of equipment, 0.40 as a result of carelessness and 0.75 as a result of sabotage. It is also felt the prior probabilities of the four causes of the explosion are 0.20, 0.40, 0.25 and 0.15. Based on all the information....
amilapsn
 one year ago
An explosion at a construction site could have occurred as the result of static electricity, malfunctioning of equipment, carelessness or sabotage. Interviews with construction engineers analysing the risks involved led to the estimates that such an explosion would occur with probability 0.25 as a result of static electricity, 0.20 as a result of malfunctioning of equipment, 0.40 as a result of carelessness and 0.75 as a result of sabotage. It is also felt the prior probabilities of the four causes of the explosion are 0.20, 0.40, 0.25 and 0.15. Based on all the information....

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amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0(a) What is the most likely cause of the explosion? (b) What is the least likely cause for the explosion?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Am I correct?: "Such an explosion would occur with probability 0.25 as a result of static electricity " \(\equiv\) P(explosion/static electricity)=0.25

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Or is it the other way round?

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0Surely "0.75 as a result of sabotage" should have been written as "0.15 as a result of sabotage". Please confirm.

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0I don't get it @kropot72

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Are you telling the given probabilities are the same?

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0The sum of the given prior probabilities is 1. The sum of the posterior probabilities must also be 1 (by the basic rule of probabilities). The most likely error in the posterior probabilities is "...0.75 as a result of sabotage". If this is written as "...0.15 as a result of sabotage", the sum of the posterior probabilities would be 1.

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0It is quite possible for the prior and the posterior probabilities of sabotage to both be 0.15.

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0But in the question it's 0.75

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Am I correct?: "Such an explosion would occur with probability 0.25 as a result of static electricity " \(\equiv\) P(explosion/static electricity)=0.25 Or is it the other way round?

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0The solution is found from Bates Theorem: \[\large P(AB)=\frac{P(A) P(BA)}{P(B)}\] for proposition A, and evidence B where P(A) is the prior, the initial degree of belief in A P(AB) is the posterior, the degree of belief having accounted for B and the quotient P(B  A)/P(B) represents the support B provides for A. So if we consider static electricity as a possible cause, the support the evidence provides for the prior is given by 0.25/0.2 = 1.25. The support for each of the other three possible causes is found in a similar way.

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0"But in the question it's 0.75" Based on the reasons in my previous posting, you need to query this part of the question with your lecturer.

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0"The solution is found from Bates Theorem:" should obviously read "The solution is found from Bayes Theorem:"

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Is this the answer: A: Static Electricity B: Malfunctioning of equipment C: Carelessness D: Sabotage E: Explosion P(EA)=0.25

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0P(EB)=0.20 P(EC)=0.40 P(ED)=0.15 (As you suggested)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0P(A)=0.20 P(B)=0.40 P(C)=0.25 P(D)=0.15

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0We have to find P(AE), P(BE), P(CE) and P(DE) right?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0P(AE)=P(A and E)/P(E), ok?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0But to find that we need to find P(E)...

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Hey I think P(ED) can be equal to 0.75...

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Because, P(EA)+P(EB)+P(EC)+P(ED) should not be 1

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0*should not necessarily be

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0The given probabilities are not posterior probabilities...

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0The first part of the question is: (a) What is the most likely cause of the explosion? So you need to find what support the evidence has on each of the prior probabilities. For static electricity the support is 1.25. For malfunction the support is 0.5. For carelessness the support is 1.6. For sabotage the support is 1 (assuming the posterior is 0.15 and not 0.75). Before taking the evidence, the leading possibilities were malfunction and carelessness, in that order. However in the light of the evidence carelessness is now the most likely cause. (b) In the light of the evidence sabotage is the least likely cause.

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0"The given probabilities are not posterior probabilities..." The last set of probabilities are given as prior probabilities. How was it concluded that the evidence based probabilities are not posterior probabilities?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Because the phrase, "...an explosion would occur with probability 0.25 as a result of static electricity..." suggests P(ExplosionStatic Electricity)=0.25 \(\sf \underline{not}\) P(Static ElectricityExplosion)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0i. e. it suggest the probability of an explosion if there is static electricity.

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0Sorry to say I need to log out now. You need to study the application of Bayes' Theorem to this kind of question. The first set of probabilities in the question are definitely posterior probabilities, based on evidence. You could find the information here helpful: https://en.wikipedia.org/wiki/Bayes'_theorem
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