A Chartered Accountant applies for a job in 2 | vedclass

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(B) Let $A$ and $B$ be the events that the chartered accountant is selected in firms $X$ and $Y$,respectively.Given: $P(A) = 0.7$,$P(\bar{B}) = 0.5$,a

Vedclass · Accepted Answer

$0.8$

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(B) Let $A$ and $B$ be the events that the chartered accountant is selected in firms $X$ and $Y$,respectively.Given: $P(A) = 0.7$,$P(\bar{B}) = 0.5$,and $P(\bar{A} \cup \bar{B}) = 0.6$.We know that $P(\bar{A}) = 1 - P(A) = 1 - 0.7 = 0.3$.Also,$P(B) = 1 - P(\bar{B}) = 1 - 0.5 = 0.5$.By De Morgan's Law,$\bar{A} \cup \bar{B} = \overline{A \cap B}$.Therefore,$P(\overline{A \cap B}) = 0.6$.This implies $P(A \cap B) = 1 - P(\overline{A \cap B}) = 1 - 0.6 = 0.4$.The probability that he is selected in at least one firm is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.$P(A \cup B) = 0.7 + 0.5 - 0.4 = 0.8$.The probability that he is selected in exactly one firm is $P(A \cup B) - P(A \cap B) = 0.8 - 0.4 = 0.4$.Wait,the question asks for the probability that he will be selected in $1$ of the firms (meaning at least one). Thus,the answer is $0.8$.

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