Question

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.

• A. $0.438$
• B. $0.538$
• C. $0.488$
• D. None of these

Answer 1

Answer: (C)

$0.488$

Let $A$ be the event that the construction job is completed on time and $B$ be the event that there is strike.

$\Rightarrow P\left(B\right)=0.65$

Hence probability that there will be no strike $=P\left(B^{\prime }\right)$

$=1-P\left(B\right)$

$=1-0.65$

$=0.35$

$\therefore P\left(B^{\prime }\right)=0.35$

By the Law of Total Probability we have $P\left(A\right)=P\left(B\right)\times P\left(A|B\right)+P\left(B^{\prime }\right)\times P\left(A|B^{\prime }\right)$

Given, $P\left(constructionjobiscompletedwithnostrike\right)=P\left(A|B\right)=0.80$

and $P\left(constructionjobiscompletedwithstrike\right)=P\left(A|B^{\prime }\right)=0.32$

$\therefore P\left(A\right)=0.65\times 0.80+0.35\times 0.32=0.488$

Hence the probability that the construction job will get complete on time is $0.488$