A problem in mathematics is given to three students A,B and C.Their chances of solving the problem are $\large\frac{1}{3}$,$\large\frac{1}{4}$ and $\large\frac{1}{5}$ respectively.Calculate the probability that the problem will be solved. - Clay6.com, a Free resource for your JEE, AIPMT and Board Exam preparation

A problem in mathematics is given to three students A,B and C.Their chances of solving the problem are $\large\frac{1}{3}$,$\large\frac{1}{4}$ and $\large\frac{1}{5}$ respectively.Calculate the probability that the problem will be solved.

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Prob at least one = 1 - Prob (not A and not B and not C) = 1 - Prob( not A ) * Prob( not B ) * Prob( not C ) = 1 - ( 1 - Prob( A ) ) * ( 1 - Prob( B ) ) * ( 1 - Prob( C ) ) = 1 - 2/3 * 3/4 * 4/5 = 1 - 2/5 = 3/5