be bound to (be or do something)
To be apt or likely to do something. We all thought that Doug was bound to be an artist, so we were very surprised when he became a trader on Wall Street. A: "Do you think it will rain today?" B: "It hasn't rained for weeks, so it's bound to."
bound to, be
Be certain or destined to; also, be determined or resolved to. For example, We are bound to hear from them soon, or No matter what they say, she is bound to run for mayor. This usage is derived from the older sense of bound as "obliged." [Mid-1500s]