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(D) Let $P(A) = 1/3$ and $P(B) = 1/4$ be the probabilities of $A$ and $B$ solving the problem.Since the events are independent,the probability that th

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Statement $- I$ is false,Statement $- II$ is true.

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(D) Let $P(A) = 1/3$ and $P(B) = 1/4$ be the probabilities of $A$ and $B$ solving the problem.Since the events are independent,the probability that the problem is solved is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Since $A$ and $B$ are independent,$P(A \cap B) = P(A) 	imes P(B) = (1/3) 	imes (1/4) = 1/12$.Therefore,$P(A \cup B) = 1/3 + 1/4 - 1/12 = (4 + 3 - 1)/12 = 6/12 = 1/2$.Statement $- I$ claims the probability is $7/12$,which is incorrect.Statement $- II$ states that the events are independent,which is a standard assumption for such problems,making Statement $- II$ true.Thus,Statement $- I$ is false and Statement $- II$ is true.

Statement $- I :$ If the probabilities of solving a problem by $A$ and $B$ are $1/3$ and $1/4$ respectively,then the probability that the problem is solved is $7/12$.
Statement $- II :$ The events described above are independent events.

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Statement $- I :$ If the probabilities of solving a problem by $A$ and $B$ are $1/3$ and $1/4$ respectively,then the probability that the problem is solved is $7/12$.Statement $- II :$ The events described above are independent events.