Earnings Per Share (Schedule of Earnings Per Share) (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended
	Jan. 31, 2019	Jan. 31, 2018
Earnings Per Share [Abstract]
Net income (loss) attributable to Cooper stockholders	$ 103.2	$ (122.5)
Basic:
Weighted average common shares	49.3	48.9
Basic earnings (loss) per share attributable to Cooper stockholders	$ 2.09	$ (2.50)
Diluted:
Effect of potential dilutive shares	0.6	0.0
Diluted weighted average common shares	49.9	48.9
Diluted earnings (loss) per share attributable to Cooper stockholders	$ 2.07	$ (2.50)