# 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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