Question 2: A particular pavement is known to fail from cracking or rutting or b

Question

Question 2: A particular pavement is known to fail from cracking or rutting or both. The pavement is forecasted to have medium truckload traffic with a probability of 0.3 and high truckload traffic with a probability of 0.7. If the pavement has medium truckload trafic, then the probability of cracking is 0.02 and rutting is 0.005. If the pavement has high truckload traffic, then the probability of cracking is 0.04 and rutting is 0.008. If the pavement has rutting, then the probability of cracking is 0.6. Determine the probability of pavement failure? Hint: Determine in the following order: (i) probability of cracking,i) probability of rutting, (iii) probability of cracking and rutting. With these probabilities you should be able to determine probability of failure

Explanation / Answer

(i) probability of cracking =P(C)=medium traffic and  cracking +high traffic and  cracking

=0.3*0.02+0.7*0.04=0.034

probability of rutting =P(R)=medium traffic and  rutting +high traffic and  rutting

=0.3*0.005+0.7*0.008=0.0071

probability of cracking given rutting =P(C|R) =0.6

therefore probability of cracking and rutting =P(C and R) =0.6*0.0071=0.00426

hence probability of failure =P(C)+P(R)-P(C and R) =0.034+0.0071-0.00426 =0.03684

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