At 15% rate, $375 will be due to the Feds. If you (or the friend, if they claim it) work another job, it's likely an excess has been withheld over the course of the year that would likely cover most, if not all, of the additional $375. Typical tax refund for many is well over $1,000.
Ohio tax is a little more tricky to calculate exactly, but figure on it being around 4%; around $100. Total tax due between state and federal being around $475 at 15% and 4% rates, respectively...
If one's federal tax rate is 25%, which is typical for many, then figure on paying $625; ~$725 total. Still, many workers receive federal tax refunds in excess of that, so there may be little to no added tax due.
Federal tax rates go high as 39.6%, and there's a 0.9% Medicare surtax above $250,000 (filing individually), so for a high-income tax filer, the total tax due, including state, could easily run 40% - 50%.
To minimize tax impact of winning, keep track of all wins and losses - not just the large ones, but all of them. Very few gamblers do that, though for the occasional gambler winning tens of thousands or less, simply claiming the amount of one's losses being equal to one's winnings will do, and likely won't be questioned. Gamblers who frequently win and deduct large amounts of losses should keep a journal - not doing so risks an audit, and being required to pay the difference, plus a penalty.
Basically, for an occasional smallish reportable win, you could simply claim your losses equal (or exceeded, but that can't be claimed) your winnings. That way you avoid paying much of the federal (and state too, depending on their rules) tax that would be due. However, to take advantage of this, one must itemize when filing and forgo the standard tax deduction - doing so is more costly for many lower income filers, and hence many can't offset losses against winnings.
As for giving a friend a winning ticket, if it's truly a gift, you have some choices ...
-- If your income is relatively high and you already itemize, claim the ticket yourself, and then give your friend the net amount after taxes. Depending on the tax calculations, you may be able to give the friend most of the $2500.
--If your income is relatively low, but your friend's income is relatively high and they already itemize, then give them the ticket for them to claim and pay tax on - they can offset their losses (setting aside the ethics of this, if they're not a regular gambler and didn't really lose that much) against winnings to minimize the tax due.
--If both your income and that of your friend are both too low to itemize, claim the ticket yourself and give your friend $2,000 cash.
* Addendum, if you and/or the friend receive various types of public assistance, claiming lottery winnings could have adverse consequences. Some get around that issue by selling their winning ticket to a third party at a sizable discount for cash on the spot. Many lotteries are on to this, but few do much, if anything about it - sure, they don't like the practice, but if they're too aggressive, they'll lose sales to other gambling venues, including offshore and illegal ones (number rackets are still around).
I'm not an accountant nor a tax preparer. There may be other scenarios to consider / better options than the above. Hope this helps.