If 85 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win 2 prizes if that person buys 2 tickets. Enter your answer as a fraction.
\[
P(\text { win both })=
\]

Step 1 ：Let's denote the number of tickets the person has as \(p\), and the total number of tickets as \(t\). In this case, \(p = 2\) and \(t = 85\).

Step 2 ：The probability of the person winning the first prize is \(\frac{p}{t}\), which is \(\frac{2}{85}\).

Step 3 ：After the first prize is awarded, the total number of tickets decreases by one, and if the person won the first prize, the number of their tickets also decreases by one. So, the new values are \(p = 1\) and \(t = 84\).

Step 4 ：The probability of the person winning the second prize is \(\frac{p}{t}\), which is \(\frac{1}{84}\).

Step 5 ：The total probability of the person winning both prizes is the product of the two probabilities calculated above, which is \(\frac{2}{85} \times \frac{1}{84} = \frac{1}{3570}\).

Step 6 ：Final Answer: The probability that one person will win 2 prizes if that person buys 2 tickets is \(\boxed{\frac{1}{3570}}\).