A) 3/4
B) 1/2
C) 2/3
D) 1/3
Correct Answer: A
Solution :
Use the relation P(A) + P \[(\overline{A})\] = 1, where P(A) = probabilities of solved question by A and P \[(\overline{A})\] = probabilities of not solved question by B. Since, probabilities of solving the problem by A, B and C are \[\frac{1}{2},\frac{1}{3}\] and \[\frac{1}{4}\], respectively. \[\therefore \] Probability that the problem is not solved \[=P(\overline{A})P(\overline{B})(\overline{C})\] \[=\left( 1-\frac{1}{2} \right)\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\] \[=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}=\frac{1}{4}\] Hence, the probability that the problem is solved \[=1-\frac{1}{4}=\frac{3}{4}\]
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