The completion time of a construction project depends on whether the carpenters

Question

The completion time of a construction project depends on whether the carpenters and plumbers working on the project will go on strike. The probabilities of delay(D) are 100% if both go on strike, and 5% if neither of them strikes. Also, there is a 60% chance that the plumbers will strike if the carpenters strike, and a 30% chance of the reverse scenario (carpenters strike following plumbers strike). The likelihood that plumbers will strike is 10% and the overall probability of a delay in completion (from any source) is 15%.

a) Are carpenter and plumber strikes independent events? Explain.

b) If there is a delay in completion, what is the probability that both carpenters and plumbers strike?

Explanation / Answer

P( Plumber strike ) = 0.1 ( given )

Also we are given that given plumbers strike, the probability that carpenter will strike is 0.3 Therefore,

P( Carpenter strike | Plumber strike ) = 0.3

Using bayes theorem we get:

P( Both strike ) / P( Plumber strike ) = 0.3

P( Both strike ) = 0.3*P( Plumber strike ) = 0.3*0.1 = 0.03

Also then we are given that given carpenters strike, the probability that plumbers will strike is 0.6 Therefore,

P( Plumbers | Carpenters ) = 0.6

Using Bayes theorem we get:

P( both strike ) / P( carpenters strike) = 0.6

Putting P( both strike ) = 0.03, we get:

0.03 / P( carpenters strike) = 0.6

Therefore,

P( Carpenters strike ) = 0.03/0.6 = 0.05

a) P( Plumbers strike ) P(Carpenters strike ) = 0.1*0.05 = 0.005

P( Both strike ) = 0.03

Therefore, as P( Plumbers strike ) P(Carpenters strike ) is not equal to P(both strike ) therefore the 2 events are not independent events here.

b) There is a 100% probability of delay if both strike, now the probability that both carpenters and plumbers strike given that there is a delay in completion is computed as:

= P( both strike and delay ) / P( Delay )

= 1*0.03 / 0.15

= 0.2

Therefore 0.2 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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