# Question

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 analyzing 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 that the prior probabilities of the four causes of the explosion are 0.20, 0.40, 0.25, And 0.15. Based on all this information, what is

(a) The most likely cause of the explosion;

(b) The least likely cause of the explosion?

(a) The most likely cause of the explosion;

(b) The least likely cause of the explosion?

## Answer to relevant Questions

Give an alternative proof of Theorem 2.7 by making use of the relationships A ∪ B = A ∪ (A' ∩ B') And B = (A ∩ B) .(A' ∩ B) . Duplicate the method of proof used in Exercise 2.12 to show that P(A ∪ B ∪ C ∪ D) = P(A) + P(B) + P(C) + P(D) - P(A ∩ B) - P(A ∩ C) - P(A ∩ D) - P(B ∩ C) - P(B ∩ D) - P(C ∩ D) + P(A ∩ B ∩ C) + P(A ∩ B ...Given three events A, B, And C such that P(A ∩ B ∩ C) Z0 And P(C| A ∩ B) = P(C| B) , show that P(A| B ∩ C) = P(A| B) . For Any event A, show that A And Ø are independent. A coin is tossed once. Then, if it comes up heads, a die is thrown once; if the coin comes up tails, it is tossed twice more. Using the notation in which (H, 2) , for example, denotes the event that the coin comes up heads ...Post your question

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