A person has undertaken a construction job. T | vedclass

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Question

(A) Let $A$ be the event that the construction job will be completed on time,and $B$ be the event that there will be a strike.We have to find $P(A)$.G

Vedclass · Accepted Answer

$0.488$

Vedclass · Answer

(A) Let $A$ be the event that the construction job will be completed on time,and $B$ be the event that there will be a strike.We have to find $P(A)$.Given:$P(B) = 0.65$$P(	ext{no strike}) = P(B') = 1 - P(B) = 1 - 0.65 = 0.35$$P(A | B) = 0.32$$P(A | B') = 0.80$Since events $B$ and $B'$ form a partition of the sample space $S$,by the theorem of total probability:$P(A) = P(B) 	imes P(A | B) + P(B') 	imes P(A | B')$$P(A) = (0.65 	imes 0.32) + (0.35 	imes 0.80)$$P(A) = 0.208 + 0.280 = 0.488$Thus,the probability that the construction job will be completed on time is $0.488$.

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