[In January, 1966] A B-52 bomber had collided with an air tanker during a refueling operation 30,000 feet in the air off the coast of Palomares, Spain, losing its atomic payload. Three of the four bombs were recovered almost immediately. But a fourth was lost and had presumably fallen to the bottom of the Mediterranean.
[Naval intelligence officer John P.] Craven called in a group of mathematicians and set them to work constructing a map of the sea bottom outside Palomeres.
Once the map was completed, Craven asked a group of submarine and salvage experts to place Las Vegas-style bets on the probability of each of the different scenarios that might describe the bomb's loss being considered by the search team in Spain. Each scenario left the weapon in a different location.
Then, each possible location was run through a formula that was based on the odds created by the betting round. The locations were then replotted, yards or miles away from where logic and acoustic science alone would place them.
[Craven] was relying on Bayes' theorem
Craven applied that doctrine to the search. The bomb had been hitched to two parachutes. He took bets on whether both had opened, or one, or none. He went through the same exercise over each possible detail of the crash. His team of mathematicians wrote out possible endings to the crash story and took bets on which they believed most. After the betting rounds were over, they used the odds they created to assign probability quotients to several possible locations. Then they mapped those probabilities and came up with the most probably site and several other possible ones.
Without ever having gone to sea, the team now believed they knew where the bomb was [...] in a deep ravine [far from where the first three bombs were recovered].
Long story short, a deep sea submersible found the bomb in that ravine, right where the calculations plotted it would be.