randomly change image of buttons and decelerate changing

i have 2 buttons.

they are called _rightButtonPressed and _leftButtonPressed. They have an background image named "blackBackground". When they are clicked, the background image is changed to "whiteBackground".

Ok. Now i want to make a third button, that changes the background image at first _rightButtonPressed to "white", then "black", then _leftButtonPressed to "white", then "black" and so on. This change have to decelerate to the end. At least, it should be randomly stops at a button with "white" background image and click the button. I hope its comprehensible.

I have no idea, how i can do this...