A problem in mathematics is given to three students P, Q and R whose chances of solving it are $$\frac{1}{3}, \frac{1}{4}$$ and $$\frac{1}{2}$$ respectively. Then the probability that the problem will be solved is:

probility of  solving problems by P, is= $$\frac{1}{3}$$

probility of not solving the problem by P , is= $$\frac{2}{3}$$

probility of solving problems by q, is= $$\frac{1}{4}$$ 

probility of not solving the problem by Q , is= $$\frac{3}{4}$$

probility of solving problems by r, is= $$\frac{1}{2}$$

probility of not solving the problem by R , is= $$\frac{1}{2}$$

so the probility of solving the problem are =problem is solved by p * problem is not solved by q and r + problem is solved by q * problem is not solved by p and r + problem is solved by r * problem is not solved by p and q + problem is solved by p and q and not solved by r + problem is solved by q and r and not solved by p + problem is solved by p and r and not solved by q + problem is solved by all three of them 

P{solved}= $$\frac{1}{3}$$* $$\frac{3}{4}$$*$$\frac{1}{2}$$ + $$\frac{1}{4}$$* $$\frac{2}{3}$$*$$\frac{1}{2}$$ + $$\frac{1}{2}$$* $$\frac{3}{4}$$*$$\frac{2}{3}$$ + $$\frac{1}{3}$$* $$\frac{1}{4}$$*$$\frac{1}{2}$$ + $$\frac{1}{4}$$* $$\frac{1}{2}$$*$$\frac{2}{3}$$ + $$\frac{1}{3}$$* $$\frac{1}{2}$$*$$\frac{3}{4}$$ + $$\frac{1}{3}$$* $$\frac{1}{4}$$*$$\frac{1}{2}$$ 

p{soleed}= $$\frac{18}{24}$$

p{solved}=$$\frac{3}{4}$$ answer 

or 

probility of not solving problems by P,Q and R are = $$\frac{2}{3}, \frac{3}{4}$$ and $$\frac{1}{2}$$ respectively 

so the probility of problem is solved is = 1-probility of not solving problems by P,Q and R are = $$\frac{2}{3}, \frac{3}{4}$$ and $$\frac{1}{2}$$

                                                         =1- $$\frac{2}{3}* \frac{3}{4}$$* $$\frac{1}{2}$$

                                                        =1-$$\frac{6}{24}$$

so the probility of problem is solved is = $$\frac{3}{4}$$