(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

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(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$$P(\text{no strike}) = P(B') = 1 - P(B) = 1 - 0.65 = 0.35$$P(A | B) = 0.32$$P(A | B') = 0.80$Since events $B$ and $B'$ form a partition of the sample space $S$,by the theorem of total probability:$P(A) = P(B) \times P(A | B) + P(B') \times P(A | B')$$P(A) = (0.65 \times 0.32) + (0.35 \times 0.80)$$P(A) = 0.208 + 0.280 = 0.488$Thus,the probability that the construction job will be completed on time is $0.488$.

Class 12 Mathematics Probability Multiplication Theorem on Probability

Medium

$A$ person has undertaken a construction job. The probabilities are $0.65$ that there will be a 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.

A
$0.488$
B
$0.512$
C
$0.320$
D
$0.800$

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Multiplication Theorem on Probability

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