14. The probability that a construction job will be finished on time is 3/5. The probability that there will be no strikes is 2/3 and the probability that the job will be finished on time given that there are no strikes is 4/5. What is the probability that the job will be finished on time and there will be no strikes? What is the probability that there were no strikes given that job is finished on time.
Answers
Answer
In a construction job, following are some probabilities given:
Probability that there will be strike is 0.65, probability that the job will be completed on time if there is no strike is 0.80, probability that the job will be completed on time if there is strike is 0.32. Determine probability that the construction job will get complete on time.
solution :
Correct option is C)
Let A be the event that the construction job is completed on time and B be the event that there is strike.
⇒P(B)=0.65
Hence probability that there will be no strike =P(B
′
)
=1−P(B)
=1−0.65
=0.35
∴P(B
′
)=0.35
By the Law of Total Probability we have P(A)=P(B)×P(A∣B)+P(B
′
)×P(A∣B
′
)
Given, P(constructionjobiscompletedwithnostrike)=P(A∣B)=0.80
and P(constructionjobiscompletedwithstrike)=P(A∣B
′
)=0.32
∴P(A)=0.65×0.80+0.35×0.32=0.488
Hence the probability that the construction job will get complete on time is 0.488