A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is \(1\over 2\), \(1\over 3\) and \(1\over 4\). Probability that the problem is solved is

Solution :

Since the probability of solving the problem by A, B and C is \(1\over 2\), \(1\over 3\) and \(1\over 4\) respectively.

\(\therefore\)  Probability that problem is not solved is

= P(A’)P(B’)P(C’)

= (\(1 – {1\over 2}\))(\(1 – {1\over 3}\))(\(1 – {1\over 4}\))

= \(1\over 2\)\(2\over 3\)\(3\over 4\) = \(1\over 4\)

= Hence, the probability that the problem is solved

= \(1 – {1\over 4}\) = \(3\over 4\)

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