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Not necessarily: consider a string of '0’s and ‘1’s’ both infinite and random.
No matter how long you look, you’ll never find a ‘2’. Same with the multiverse, not all things need to exist.
I was about to make a comment about, how a double pendelum can swing in an infinite amount of unpredictable ways, none of which will suddenly turn it into a car. But I like your analogy so much better.