Two students Anil and Ashima appeared in an e | vedclass

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(A) Let $E$ and $F$ denote the events that Anil and Ashima will qualify the examination,respectively.Given that $P(E) = 0.05$,$P(F) = 0.10$,and $P(E \

Vedclass · Accepted Answer

$0.87$

Vedclass · Answer

(A) Let $E$ and $F$ denote the events that Anil and Ashima will qualify the examination,respectively.Given that $P(E) = 0.05$,$P(F) = 0.10$,and $P(E \cap F) = 0.02$.The event 'both Anil and Ashima will not qualify the examination' is represented as $E' \cap F'$.By De Morgan's Law,$E' \cap F' = (E \cup F)'$.First,we calculate the probability that at least one of them qualifies:$P(E \cup F) = P(E) + P(F) - P(E \cap F)$$P(E \cup F) = 0.05 + 0.10 - 0.02 = 0.13$.Now,the probability that neither qualifies is:$P(E' \cap F') = P((E \cup F)') = 1 - P(E \cup F)$$P(E' \cap F') = 1 - 0.13 = 0.87$.

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