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The probability that an airplane accident due to structural failure is diagnosed correctly is 0.72, and...

The probability that an airplane accident due to structural failure is diagnosed correctly is 0.72, and the probability that an airplane accident which is not due to structural failure is diagnosed incorrectly as being due to structural failure is 0.12. If 40 percent of all airplane accidents are due to structural failure, what is the probability that an airplane accident which is diagnosed as being due to structural failure is actually due to this cause?

Please draw the tree diagram when showing the answer. Thank you

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Answer #1

here let probability of accident due to structure failure is P(S) and diagnosed as structure failure =P(D)

P/SnD)=0.288 0.288 PIDIS)=0.72 P(DC|S)=0.28 P(S)=0.4 P(SnDc)=0.112 0.112 P/ScnD)=0.072 0.072 P/Sc)=0.6 P/DSC)-0.12 P(Dc Sc)=0

probability that an airplane accident which is diagnosed as being due to structural failure is actually due to this cause

=P(S|D) =P(S n D)/P(D) =0.4*0.72/(0.4*0.72+0.6*0.12)=0.8

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