It's a novelty or magician's coin, NOT a Mint error, it may also be a home-made glued together coin, none have any numismatic collectible value.
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Double headed novelty and Magician's coins have no numismatic value, but depending on the denomination an quality most are under $10.00.
There is the probability of 1/2 if it is a fair coin. There is the probability of 1 if it is a double-headed coin. There is the probability of 0 if it is a double-tailed coin.
The simple answer is, You Don't. It's a fake. If you use the Search feature of this site (enter the word DOUBLE) you'll find hundreds of similar questions about these privately-made novelty items.
The same as all other double-headed coins - nothing. It's a trick coin sold at novelty shops for a couple of bucks. It's not real and has no value to collectors.
No, it's not possible that a double-headed quarter with two such diverse dates could be a legitimate Mint error. Dies are destroyed, if not worn out through usage, by the end of the year in which they are used. The coin in question is almost certainly a novelty or magician's coin.