In the 19th century, the majority of the workers in Japan`s modern industries were mainly women. This means that option 1, which states that the workers were Japanese men and children, is incorrect.

Option 2 suggests that the majority of the workers were Japanese women and Chinese men, but this is not accurate according to the information provided. While it is possible that there were some Chinese men working in Japan`s industries, the answer implies that the primary workforce consisted of women. Therefore, option 2 is also incorrect.

Option 4 states that the majority of the workers were Japanese and Chinese men. Again, while it is possible that there were some Chinese men working in Japan`s industries, the main focus here is on the role of women as workers. Option 4 does not reflect this, so it is incorrect as well.

The correct answer provided is option 3, that the majority of the workers in Japan`s modern industries in the 19th century were women. This means that women played a significant role in contributing to Japan`s industrial development during this time period.