The correct answer is option 4, Hepatitis A. Hepatitis A is not caused by a bacteria but by a virus. The other three options, Cholera, Typhoid, and Bacillary dysentery, are caused by bacteria.

Cholera is caused by the bacteria Vibrio cholerae, which is typically transmitted through contaminated water and food. It leads to severe diarrhea and dehydration.

Typhoid fever is caused by the bacteria Salmonella typhi, which is often transmitted through contaminated water and food. It causes high fever, abdominal pain, and diarrhea.

Bacillary dysentery, also known as shigellosis, is caused by the bacteria Shigella spp. It spreads through contaminated food and water and causes severe diarrhea with blood and mucus.

In contrast, Hepatitis A is caused by the Hepatitis A virus (HAV). It is usually spread through contaminated food, water, or close contact with an infected person. Hepatitis A infects the liver and can cause flu-like symptoms, jaundice, and liver inflammation.

Therefore, when it comes to water-borne diseases, Hepatitis A is the only option that is not caused by bacteria.