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?