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Omni-MATH / Ellie's drawer of hair clips contains 4 red clips, 5 blue clips, and 7 green…

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problem

Ellie's drawer of hair clips contains 4 red clips, 5 blue clips, and 7 green clips. Each morning, she randomly chooses one hair clip to wear for the day. She returns this clip to the drawer each evening. One morning, Kyne removes kk hair clips before Ellie can make her daily selection. As a result, the probability that Ellie chooses a red clip is doubled. What is a possible value of kk?
Plain-text mathematical notation (without MathML)
Ellie's drawer of hair clips contains 4 red clips, 5 blue clips, and 7 green clips. Each morning, she randomly chooses one hair clip to wear for the day. She returns this clip to the drawer each evening. One morning, Kyne removes k hair clips before Ellie can make her daily selection. As a result, the probability that Ellie chooses a red clip is doubled. What is a possible value of k?
Original LaTeX notation
Ellie's drawer of hair clips contains 4 red clips, 5 blue clips, and 7 green clips. Each morning, she randomly chooses one hair clip to wear for the day. She returns this clip to the drawer each evening. One morning, Kyne removes $k$ hair clips before Ellie can make her daily selection. As a result, the probability that Ellie chooses a red clip is doubled. What is a possible value of $k$?

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