There's a gun located on an infinite line. It starts shooting bullets along that line at the rate of one bullet per second. Each bullet has a velocity between 0 and 1 m/s randomly chosen from a uniform distribution. If two bullets collide, they explode and disappear. What is the probability that at least one of the bullets will infinitely fly without colliding with another bullet?

There's a gun located on an infinite line. It starts shooting bullets along that line at the rate of one bullet per second. Each bullet has a velocity between 0 and 1 m/s randomly chosen from a uniform distribution. If two bullets collide, they explode and disappear. What is the probability that at least one of the bullets will infinitely fly without colliding with another bullet?

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