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.
i) What is the probability that the job will be finished on time and there will be no strikes?
ii) What is the probability that there are no strikes given that the job is finished on time?
Answer:
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Answer:
0.488
Step-by-step explanation:
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