Three road construction firms, X , Y , and Z, bid for a certain contract. From p

Question

Three road construction firms, X , Y , and Z, bid for a certain contract. From past experience, it is estimated that the probability that X will be awarded the contract is 0.40, while for Y and Z the probabilities are 0.35 and 0.25 respectively. If X does receive the contract, the probability that the work will be satisfactorily completed on time is 0.75. For Y & Z these probabilities are 0.80 and 0.70. It turns out that the work done satisfactorily. (a) what is the probability that Y was awarded the contract? (b) what is the probability that the work will be completed satisfactorily?

(c)  what is the probability that Y was awarded the contract and complete the work satisfactorily?

Explanation / Answer

a) probability that Y was awarded the contract given work done satisfactorily

=P(Y was awarded and  work done satisfactorily)/P(work done satisfactorily)

=(0.35*0.8)/(0.4*0.75+0.35*0.8+0.25*0.7)=0.3709

b)

probability that the work will be completed satisfactorily =P(awarded to X and completed satisfactorily+awarded to Y and completed satisfactorily+awarded to Z and completed satisfactorily)

=0.4*0.75+0.35*0.8+0.25*0.7 =0.755

c) probability that Y was awarded the contract and complete the work satisfactorily =0.35*0.8 =0.28

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.