I always thought about this whenever I saw Harry Potter movies or read books, that where exactly magic lies? Is it in wizards or wands? As mentioned in Harry Potter and the Philosopher's Stone, Harry is able to make the glass disappear. Then in Harry Potter and the Prisoner of Azkaban he blows away his aunt without even touching the wand. So if magic is possible without wands why do they need it in the first place? Also, Ollivander tells Harry that wand chooses the wizards, so does wand actually have magic? Kindly help.
Magic is possessed by Wizards, of course. But, a Wand is required to focus and channel magic.
However, exceptionally gifted wizards are sometimes able to do accidental wandless magic.
When I read your question I thought of what Hagrid said to him in the very first book,"You're a wizard, Harry." Wizards have wizard blood as opposed to muggle blood. Even if a person has part wizard blood and part muggle, they will still have wizard abilities like Hermione Granger (a half-blood). Muggles do not have the ability to use magic.