Question

Event A represents the delay in completion of a construction project. This event depends on the shortage of two basic materials, timber and concrete in the market. Let T=event that there is a shortage of timber in the market and P(T)=0.15; and C=event that there is a shortage of concrete in the market and P(C)=0.20. Furthermore, we know that if there is a shortage of timber, the probability that for the same reason there is concrete shortage is 0.4 . On the other hand, if there is a shortage of both timber and concrete, the probability of delay is 0.8 . If only one of the two materials has a shortage, the probability of delay is 0.5 . We are approaching the construction season and do not know what would be the situation with the availability of the two materials.

(a) Based on the information give, compute the probability that the project will be delayed because of material shortage.
(b) If it is certain there will be a delay, compute the probability that the cause is shortage of concrete onl

Answer 1

To compute the probability of delay due to material shortage in a construction project, we can use the law of total probability. However, without knowing the probability of shortage of both timber and concrete, we cannot calculate the exact probability.

Step-by-step explanation:

In order to compute the probability that the project will be delayed due to material shortage, we can use the law of total probability. There are two possible scenarios: either there is a shortage of timber or there is a shortage of concrete.

If there is a shortage of timber, the probability is P(T)=0.15. If there is a shortage of concrete given a shortage of timber, the probability is P(C|T)=0.4. Finally, if both timber and concrete are in shortage, the probability of delay is 0.8.

So we can calculate the probability of delay as follows:

P(Delay) = P(T) * P(C|T) + P(T and C) = 0.15 * 0.4 + P(T and C)

Now, since we do not know the probability of shortage of both timber and concrete, we cannot solve for P(T and C). Therefore, we cannot compute the exact probability of delay due to material shortage.