Is it possible to connect arduino pro with an android phone with a usb cable?
Yes, it is possible if the phone supports USB OTG. FTDI have Android drivers on their website. It should be even possible to access it like a normal serial port, details are here

The connector is not mini-b, this is micro-b (the board) and micro-ab (the phone). You need OTG cable with micro-a and micro-b such as this.