What really happened — and how likely is it that there's no natural explanation?

On 4 July 1976, Israeli commandos flew over 4,000 kilometres to Entebbe Airport, Uganda, stormed the terminal in under an hour, and rescued 102 hostages held at gunpoint by Palestinian and German hijackers — an outcome widely described as a miracle.

Between 1993 and 2010, Joan R. Ginther — a Stanford-trained mathematician born in Bishop, Texas — won four separate Texas lottery prizes totaling $20.4 million, a run of fortune so statistically extreme it prompted serious investigation into whether luck alone could explain it.

On 26 January 1972, flight attendant Vesna Vulović survived when JAT Yugoslav Airlines Flight 367's DC-9 broke apart over Czechoslovakia — officially at 10,160 m (33,330 ft), earning the Guinness World Record for the highest fall survived without a parachute, though a 2009 journalistic investigation argues the aircraft was near 800 m when it disintegrated.

Anita Moorjani, a Hong Kong businesswoman who had refused conventional treatment for Hodgkin lymphoma for nearly four years, was admitted to Hong Kong Sanatorium & Hospital in early February 2006 in organ failure, weighing about 36 kilograms, and fell into a 30-hour coma during which she reports a near-death experience; her physicians drained her fluid-filled chest and began chemotherapy while she was comatose, her tumors shrank by well over half within days, and she left the hospital cancer-free in five weeks — a recovery her treating oncologist attributed to the chemotherapy and the emergency drainage, and her bestselling memoir attributes to the experience.

Annabel Beam, a Texas nine-year-old who had spent most of her childhood under specialist care for two incurable digestive motility disorders, fell about 30 feet headfirst into the hollow trunk of a cottonwood tree in December 2011 and was lifted out essentially uninjured five hours later. In the months that followed her symptoms were gone; Boston Children's Hospital eventually released her from gastroenterology care, her treating specialist confirmed the resolution on the record, and the story became the book and 2016 film Miracles from Heaven.

Bahia Bakari, a 12-year-old from Évry, France, who could barely swim, was the only survivor among 153 people aboard Yemenia Flight 626 when it crashed into the Indian Ocean on night approach to Moroni, Comoros, on June 30, 2009; she clung to floating wreckage for at least nine hours in heavy seas until a sailor from the ferry Sima Com 2 jumped in to reach her, and thirteen years later she testified at the Paris trial that convicted the airline of involuntary manslaughter.