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Question

(A) Let $P(A)$ be the probability that person $A$ completes the work,$P(A) = \frac{2}{3}$.Let $P(B)$ be the probability that person $B$ completes the

Vedclass · Accepted Answer

$\frac{11}{12}$

Vedclass · Answer

(A) Let $P(A)$ be the probability that person $A$ completes the work,$P(A) = \frac{2}{3}$.Let $P(B)$ be the probability that person $B$ completes the work,$P(B) = \frac{3}{4}$.The work is completed if at least one of them completes the work.This is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Since the events are independent,$P(A \cap B) = P(A) 	imes P(B) = \frac{2}{3} 	imes \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$.Therefore,$P(A \cup B) = \frac{2}{3} + \frac{3}{4} - \frac{1}{2}$.Finding a common denominator of $12$:$P(A \cup B) = \frac{8}{12} + \frac{9}{12} - \frac{6}{12} = \frac{11}{12}$.Thus,the probability that the work is completed is $\frac{11}{12}$.

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