you're talking about price. So yeah that is entirely in the realm of possibility. You should know that Bitcoin started out worthless basically until someone nervously helped ordered 2 boxes of pizza for someone who gave them 20,000 BTC for the effort.
At the time it was the guy who received the 20,000 BTC that was taking a gamble. He basically did it for free since no one is buying and selling Bitcoin at that point (2010).
If enough people decided something is worthless, it will be worthless. Ever heard of the Beanie Baby? it was all the rage back in the 90's and people really did forfeit on mortgages to buy those stuff with reckless abandon. Now those dolls are literally worthless.
I guess your question though would be "What are the chance of Bitcoin price becoming zero in my lifetime?" right?
You need to understand the "Diffusion of innovation" theory that charts how a new technology gets spread to the masses as it hits 100% marketshare. Basically, the price of Bitcoin is propped by hype and speculation, like almost any other bubble in the world right now. Practically speaking though, Bitcoin as a means of MOE and SOV is still largely unknown to the regular Joe. I can confidently say that even you yourself dont really the full extent of what bitcoin can do. When enough people finally realized how powerful Bitcoin is than just a speculative asset, I think thats when the perceived value of Bitcoin will soar and volatility decreases.
So no, It's hard to see how bitcoin can go worthless anytime soon.
Of course they can be worthless. Cryptos (like stocks) are driven by demand and supply (and speculation), and thus if there is no demand for Bitcoin, or if there is a major hack or government crack down then it could lead the price down to basically nothing. Bitcoins would only become worthless if there were no longer any buyers, as demand had dried right up. This has happened in the stock market before, where major companies have gone from worth billions to bust Enron is the biggest example, whcih was one of the biggest companies in America, but went belly up due to a wide spead scandal.
It is not likely though, as there are to many major players and investors involved for the market to take such a significant crash down to zero. Being decentralised also means that it not likely that there will be any internal manipulation, and fraud (Such as can happen in stocks). However, if the government cracks down on crypto then it could have a massive effect
Being that Bitcoin is a cryptocurrency, and crypto is driven by speculation, the answer is simply no. Bitcoins will never be worthless, as long as someone desires to have them, and given that they are a scarce digital asset, it is likely that someone will always want Bitcoin. For a further understanding of speculation in regards to crypto, this link to wikipedia may help you.
I hope this answer helps!