"I had a strange coincidence today."
Yuki began talking.
"What kind?" Riku asked.
"I bumped into someone at the station, and they're a transfer student. Coming to our class tomorrow."
Aoi was interested. "Interesting coincidence."
"Was it coincidence?" Yuki thought.
"Probabilistically, what do you think?"
Aoi started calculating. "Number of people at the station, number of transfer students, class size..."
"Quite low probability. But not zero."
Riku interrupted. "Even low probability happens when it happens."
"That's the essence of randomness."
Yuki asked. "But can I call it a miracle?"
"Subjectively, yes. When low-probability events occur, they feel special."
Aoi explained. "Information content is I(x) = -log₂(p). Lower probability p, larger information content."
"That's why rare events stay in memory."
Riku gave an example. "Like winning the lottery."
"Probability is extremely low. But someone wins."
"Seen overall, it's inevitable."
Yuki thought. "Then my encounter was bound to happen to someone?"
"Statistically, yes."
Aoi continued. "But that it was you has meaning."
"Randomness doesn't choose who it happens to."
Riku asked. "Is random really random?"
"Philosophical question."
Aoi thought. "In quantum mechanics, true random numbers exist."
"But daily coincidences might be results of complex causation."
"Deterministic chaos. Small differences in initial conditions cause large result changes."
Yuki wrote in her notes. "Then me being at the station at that time was also causation?"
"Traced back, it's accumulation of countless choices."
"What time I woke up. Which train I took."
Riku laughed. "Butterfly effect."
"Small changes create large results."
Aoi supplemented. "But tracking all that is impossible."
"So we treat it as random."
"Approximate with probability models."
Yuki asked. "Coincidence or inevitability, which is real?"
"Both," Aoi answered.
"Changes with perspective."
"From an omniscient view, all is inevitable. But with limited knowledge, it seems random to us."
Riku nodded deeply. "That's why probability theory is needed."
"Mathematics handling uncertainty."
Aoi presented a new perspective. "There's a concept called expected value."
"E(X) = Σ x・p(x). Average of random variables."
"Repeated trials approach expected value."
Yuki thought. "Then if I go to the station many times, coincidences will happen again?"
"Expectation-wise, eventually."
"But not the same coincidence."
Riku said. "Each coincidence is one-time."
"Unique."
Aoi smiled. "That's why coincidences are special."
"They have value because they can't be reproduced."
Yuki summarized. "Randomness brings encounters."
"Can't be planned or predicted."
"But that's why they feel miraculous."
Riku suddenly asked. "Then our meeting was also random?"
"The choice to join the information theory club?"
Aoi answered. "Partly random. But partly inevitable."
"Your personalities, interests, timing of seeing the notice."
"Everything overlapped and brought you here."
Yuki looked out the window. "Countless coincidences create now."
"And now becomes seeds of future coincidences."
Riku laughed. "Sounds romantic."
"The miracle that randomness brought."
Aoi concluded. "Probability theory seems like cold mathematics."
"But behind it are life's dramas."
"Coincidence and inevitability, randomness and meaning."
"We live at that boundary."
The three nodded quietly.
Tomorrow, new coincidences will bring someone again. That too is randomness's miracle.