Bull's-eye!

As per British Darts Organisation (BDO), the standard dart board used in international competitions has an overall diameter of \(45.1\text{ cm}\), and an inner bull's-eye (red circle in the center) diameter of \(12.7\text{ mm}\).

Assuming that all shots fall within the dart board area, what is the expected number of attempts needed for the player to hit the inner bull's-eye area once?

Round off your answer to the nearest whole number.

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