Q.A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 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.

Use the law of total probability: the job is completed on time either via the strike branch or the no-strike branch, weighted by how likely each branch is.

Let $S$ = "there is a strike" and $T$ = "job completed on time." Given:

$P(S)=0.65 \quad\Rightarrow\quad P(S')=1-0.65=0.35,$

$P(T\mid S')=0.80 \quad\text{(on time, no strike)},$

$P(T\mid S)=0.32 \quad\text{(on time, despite strike)}.$

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