A person has undertaken a construction job. The probabilities are `0.80` that there will be a strike, `0.70` that the construction job will be completed on time if there is no strike, and `0.4` that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.

Explanation

Let A be the event "the construction job will be completed on time" and B be the event "there will be a strike"
According to the question,
P (B) =0.8
`therefore` P(B') = P (there will be no strike) = 0.2
Also, P(A/B')= P (construction job will be completed on time if there is no strike) `=0.7` and P(A/B) = P (construction job will be completed on time of there is a strike) `=0.4`
Using total probability theorem, we get
`P(A)=P(B)P(A//B)+P(B')P(A//B')`
`=0.8xx0.4+0.2xx0.7`
`=0.32+0.14`
`=0.46`