On Debian-based systems (which of course include Ubuntu, Lubuntu, Kubuntu, Xubuntu), and by extension, Peppermint Two, which is derived directly from Lubuntu), the following Debian Wiki page is of great help: http://wiki.debian.org/bcm43xx
On that page, it is pointed out that the firmware-b43-installer package will normally do everything required, including probing for the correct firmware module, once installed. In my case, apparently on Peppermint Two, something was already "there", either installed or configured in a way that created a conflict with the expected behavior. The Wiki page listed above also covers work around behavior to account for issues with module probing.
In case of difficulties, these steps, described on the Wiki page, should resolve the conflict:
The necessary kernel module should be automatically loaded. If necessary, it can be manually loaded via either:
Verify your device has an available interface:
Raise the interface to activate the radio, for example:
ifconfig wlan0 up
If that still does not immediately resolve the issue, then
modprobe -r b43
echo options b43 pio=1 qos=0 >> /etc/modprobe.d/local.conf
should take care of it.