They still wonder why they lived when so many others died. Each of them counts many small items of chance or volition—a step taken in time, a decision to go indoors, catching one streetcar instead of the next that spared him. And now each knows that in the act of survival he lived a dozen lives and saw more death than he ever thought he would see. At the time, none of them knew anything. (1.1)
Hersey describes where each of his subjects was during the blast in pretty painstaking detail, which really drives home how much pure luck/chance figured in ensuring their survival. This early passage really sets us up to think about this notion of chance and its importance as we read about those who survived—and those who didn't.
Dr. Fujii hardly had time to think that he was dying before he realized that he was alive, squeezed tightly by two long timbers in a V across his chest, like a morsel suspended between two huge chopsticks—held upright, so that he could not move, with his head miraculously above water and his torso and legs in it. (1.18)
Although you wouldn't typically think of being pinned between two beams as lucky, Dr. Fujii actually was pretty fortunate to get stuck with his head above water. Again, dumb luck seems to have contributed a fair amount to the survival of the six main subjects.
At the terminus, he caught a streetcar at once. (He later calculated that if he had taken his customary train that morning, and if he had had to wait a few minutes for the streetcar, as often happened, he would have been close to the center at the time of the explosion and would surely have perished.) (1.25)
Dr. Sasaki has his own tales (yes, plural) of near death. In his first "lucky" stroke, he didn't end up waiting long for a streetcar (as was often the case), which means he wasn't super close to the center of town when the bomb was dropped.
Dr. Sasaki found himself the only doctor in the hospital who was unhurt. (1.26)
In a second lucky stroke for Dr. Sasaki, he ended up being positioned within the walls of the hospital such that he ended up the only uninjured doctor there… which is pretty crazy, when you think about it.
Mr. Tanimoto climbed up the bank and ran along it until, near a large Shinto shrine, he came to more fire, and as he turned left to get around it, he met, by incredible luck, his wife. She was carrying their infant daughter. Mr. Tanimoto was now so emotionally worn out that nothing could surprise him. (2.35)
If a fictional story included all the coincidences and chance meetings that occur in this true account of the Hiroshima attacks, you probably wouldn't believe it. Here, we learn that Mr. Tanimoto ended up running into his wife, despite the fact that Hiroshima was a large city (and, you know, thrown into total chaos after the attack). Incredible, right?
Judging by the many maimed soldiers Mr. Tanimoto had seen during the day, he surmised that the barracks had been badly damaged by whatever it was that had hit Hiroshima. He knew he hadn't a chance of finding Mrs. Kamai's husband, even if he searched, but he wanted to humour her. "I'll try," he said. (2.56)
Despite the fact that some incredible/lucky things had happened to him since the bomb dropped (for example, randomly running into his wife amid all the chaos without having to go searching for her), Mr. Tanimoto was not feeling so sure that Mrs. Kamai's husband was going to turn up. In fact, he believed "he hadn't a chance of finding" him. So, you kind of get a sense with this passage that there was a fair amount of despair/fatalism going on.
Mrs. Nakamura had gone to the city again, to dig up some rice she had buried in her Neighborhood Association air-raid shelter. She got it and started back for Kabe. On the electric car, quite by chance, she ran into her younger sister, who had not been in Hiroshima the day of the bombing. (3.58)
Again, as with the story of Mr. Tanimoto randomly meeting his wife on the street the day of the bombing, it's kind of incredible that Mrs. Nakamura would run into her sister so randomly. By drawing attention to these incidents, Hersey really does point out the randomness of basically everything.
If fever remained steady and high, the patient's chances for survival were poor. The white count almost always dropped below four thousand; a patient whose count fell below one thousand had little hope of living. […] Some victims recovered in a week; with others the disease dragged on for months. (4.17)
In a fairly extensive discussion of how doctors viewed/treated patients suffering from the bomb's aftereffects, Hersey spotlights the randomness of survival/thriving among patients. Hersey starts out by drawing a direct relationship between fever/white count and survival, but by the end of this paragraph, he basically indicates it was a matter of pure chance whether people were going to thrive or not; some people lasted a week and others for months.
And, as if nature were protecting man against his own ingenuity, the reproductive processes were affected for a time; men became sterile, women had miscarriages, menstruation stopped. (4.18)
While most of the time Hersey's narrative seems to be pointing out randomness and chance, here he veers in the other direction and suggests that the reproductive problems men and women suffered after the bomb almost seemed "intentional"—or, at least, designed protect the human race from perpetuating the kind of destruction/destructive behavior associated with the bomb. Of course, we know he doesn't mean that literally, but the mere suggestion once again gets us thinking about the notions of fate, destiny, chance, and intention, and how they relate to something like atomic war…
The bombing almost seemed a natural disaster—one that it had simply been her bad luck, her fate (which must be accepted) to suffer. (5.6)
Mrs. Nakamura wasn't super interested in ruminating on her plight as a survivor of the Hiroshima attacks or thinking much about the event's meaning in terms of global politics; she treated the bombing not as something that was intentional/preventable, but rather a freak occurrence that "it had simply been her bad luck" and "fate" to endure.