25 An integer is chosen from the set $\{1,2,3, \ldots, 499,500\}$. The probability that this integer is divisible by 7 or 11 is $\frac{m}{n}$ in its lowest terms. Find the value of $m+n$.
25. Answer: 61
There are 71 multiples of 7,45 multiples of 11 and 6 multiples of 77 that are less than 500 . So there are $71+45-6=110$ numbers in the set which are multiples of 7 or 11 . Hence probability $=\frac{110}{500}=\frac{11}{50}$.