A problem is given to 3 students A, B and C whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the chance that the problem is solved.
Choose one:  A) 2/3  B) 1/2  C) 1/4  D) 3/4  E) 3/7
Explanation :   P(A) = 1/2, P(~A) = 1 - (1/2) = 1/2. [ Prob. of not solving A ]   P(B) = 1/3, P(~B) = 1 - (1/3) = 2/3. [ Prob. of not solving B ]   P(C) = 1/4, P(~C) = 1 - (1/4) = 3/4. [ Prob. of not solving C ]   The problem is solved means atleast one of A,B and C will solve the problem.   Whenever 'at least one' is present it is easier to do the problem by using the complement of the event (opposite of the event i.e problem not solved )   P (problem is not solved)   = P(~A~B~C)   = P(~A) x P(~B) x P(~C).   = (1/2) x (2/3) x (3/4).   = 1/4.   P (problem is solved i.e atleast one solves)   = 1 - P(~A~B~C).   = 1 - (1/4).   = 3/4.   Answer : 3/4
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A problem is given to 3 students A, B and C whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the chance that the problem is solved.