A civil engineering company, based on past experience, believes that in 40% of c

Question

A civil engineering company, based on past experience, believes that in 40% of cases bridges collapse due to construction problems, 45% of cases bridges collapse due to design problems, and 15% of cases bridges collapse due to other problems such as earth quakes, heavy vehicular laods etc. Danny is a good designer and claims that there is only log(DGC)=2.5%=0.025 chance that his design may fail, and also chris is a good constructor and claims that there is only 0.5log(DGC)=1.26%=0.0126 chance that his construction may collapse, and assume other 15% of collasping remain the same. Assume the construction company bought a design from danny and later hired chris as constructor. Unfortunately, the suspension bridge collapsed within the warranty period.

(a). What is the consditional probability that the bridge collasped due to design problem?

(b) what is the conditional prbability that the bridge collapsed due to construction problem?

Explanation / Answer

P(Collapse due to construction problem) = 0.4
P(Collapse due to design problem) = 0.45
P(Collapse due to other problem) = 0.15

P(Danny design will fail)=0.025
P(Chris construction will collapse)=0.0126

P(Bridge Collapse) = 0.4 * 0.0126 + 0.45*0.025 + 0.15 = 0.166

a)

P(Collapse due to design problem / Bridge Collapse) = (0.45*0.025)/0.166 = 0.0678 Answer

b)

P(Collapse due to construction problem / Bridge Collapse) = (0.4 * 0.0126)/0.166 = 0.0303 Answer

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