Mouse Entered is supposed to be triggered when the mouse enters the component. In case of Choice, a mouse entered followed by a mouse exit is triggered when the mouse enters the component. Similarly when the mouse leaves the component a mouse entered followed my mouse exit events are triggered. Actually Mouse Entered is triggered when the mouse enters the border of the choice component and a Mouse Exit is triggered when the mouse leaves the border regardless of whether the mouse is going into /away from the component. When the mouse is moved towards the clickable arrow from within the component, mouse entered is triggered when mouse is already inside the component.
I am able to reproduce this on JDK1.5.0 - b04 as well as in Mantis b19.
This is specific to Solaris and not reproducible on Windows.

How to reproduce:
I have attached a sample code. Execute it. You would see a frame with a choice added to the southern region of it's border layout. Move the mouse over choice slowly and keep an eye on the console. All the mouse events triggered are printed to the console. You would see the above behaviour where mouse exited will be triggered when the mouse actually goes into the component.