Problem:
In a school competition,the probability of hitting the target bu Dick is $\frac{1}{2}$,by Betty is $\frac{1}{3}$ and by Joe is $\frac{3}{5}$.If all of them fire independently,calculate the probability that the target will be hit.
This general approach for solving is to find the complement of the probability that the target would not be hit.
What I am not getting is that if the there events are mutually exclusive/independent then why not summing the three probabilities doesn't gives the correct answer?!
Please explain.