Question

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The settlement problem of a steel frame may be idealized as follows. A and B represent two ootings resting on soil. Each footing may either remain at the original level or settle 5 cm. The robability of settlement in each footing is 0.1. However, the probability that a footing will settle iven that the other has settled is 0.8. Find the possible combinations of the footings conditions ナAssume E is the event of differential settlement (that is, a difference in the level of the two footings). What is the probability of E?

Answer 1

let probability of A and B to be settle is P(A) and P(B)

and not to settle are P(A') and P(B')

hence from above P(A)=P(B)=0.1 and P(A|B)=0.8 ; P(B|A)=0.8

hence P(A B)=P(A)*P(B|A)=0.1*0.8 =0.08

a) possible combinations are:

both A and B settled :AB

A settled and B remain at original :A B'

A remain at original and B settled :A' B

A and B both remain at original: A' B'

b)

P(AB)=0.08

P(AB')=P(A)-P(AB)=0.1-0.08=0.02

P(A'B)=P(B)-P(AB)=0.1-0.08=0.02

P(A' B')=1-P(A u B) =1-(P(A)+P(B)-P(A n B))=1-(0.1+0.1-0.08)=0.88

c)

P(E)=P(AB')+P(A'B) =0.02+0.02=0.04