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(A) Let $A$ and $B$ be the events of passing English and Hindi examinations respectively.Given: $P(A \cap B) = 0.5$ and $P(A' \cap B') = 0.1$.We know

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$0.65$

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(A) Let $A$ and $B$ be the events of passing English and Hindi examinations respectively.Given: $P(A \cap B) = 0.5$ and $P(A' \cap B') = 0.1$.We know that $P(A \cup B)' = P(A' \cap B') = 0.1$ by De Morgan's law.Therefore,$P(A \cup B) = 1 - P(A \cup B)' = 1 - 0.1 = 0.9$.We also know the formula: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Given $P(A) = 0.75$,we substitute the values:$0.9 = 0.75 + P(B) - 0.5$.$0.9 = 0.25 + P(B)$.$P(B) = 0.9 - 0.25 = 0.65$.Thus,the probability of passing the Hindi examination is $0.65$.

The probability that a student will pass the final examination in both English and Hindi is $0.5$ and the probability of passing neither is $0.1$. If the probability of passing the English examination is $0.75$,what is the probability of passing the Hindi examination?

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