One mathematician = ten divisions In World War II, in order to fight against Germany and France, a large number of munitions had to be transported across the Atlantic to various battlefields. However, before 1934, the British and American fleets responsible for transporting goods were often attacked by German submarines and suffered heavy losses. At that time, Britain and the United States were limited by their strength and could not send more escort ships. At that time, Germany's "submarine war" overwhelmed the allies, and maritime transportation became a headache.

At this dilemma, an American navy general went to consult several mathematicians.

Mathematicians found that the encounter between a transport fleet and an enemy submarine is a random event, that is, whether the fleet is attacked depends on whether it meets an enemy submarine during the voyage, but it may or may not happen. From a mathematical point of view, this problem has certain rules.

1. A certain number of ships, the smaller the formation size, the more batches; The more batches, the greater the probability of encountering enemy submarines.

For example, five students go back to their own homes after school, and the teacher can find a classmate and go to any classmate's home. But if these five students are all concentrated in one of them's home, the teacher may have to find several to find them, and the possibility of finding them at one time is only one in five, that is, 20%.

2. Once encountering an enemy submarine, the smaller the fleet, the greater the possibility that each ship will be hit.

This is because the number of German submarines is always small compared with the number of fleets, and the ammunition carried by submarines is limited. Every attack, no matter how big the fleet is, the number of submarines sunk is basically the same.

If the total number of transport ships is 100 and each team has 20 ships, it will be organized into 5 teams; According to the formation of each team 10 ships, it is necessary to form 10 teams. The probability ratio of two formations meeting enemy submarines is 5: 10, that is, 1: 2.

Assuming that five transport ships are lost every time they are attacked by enemy submarines, the ratio of the probability of each ship being hit in the above two formation modes is 5/20: 5/ 10 = 1: 2.

On the whole, the probability ratio of each transport ship encountering an enemy submarine and sinking in the two formation modes is 1: 4. This shows that 100 transport ship is less dangerous than 10 transport ship.

On the advice of mathematicians, the US Navy improved the practice of setting sail for transport ships from various ports, and ordered the fleet to assemble in the designated sea area, then collectively pass through the dangerous sea area and then sail to the scheduled port.

Miracle appeared, and the probability of the allied fleet being attacked and sunk dropped from 25% to 1%, which greatly reduced the losses and ensured the supply of strategic materials.

Thus, the US military declared that the role of an excellent mathematician is more than the strength of ten divisions!