Option 1 states that discontinuous variations appear suddenly or accidentally. Discontinuous variations are actually caused by changes in the genes, which can occur due to mutation or recombination. These variations are not accidental, but rather a result of genetic changes.

Option 2 states that continuous variations are caused by environmental changes. Continuous variations, however, are actually caused by the interaction of multiple genes and environmental factors. They do not occur solely due to environmental changes.

Option 3 states that Mendel is known as the Father of Genetics. This is correct. Gregor Mendel is credited with discovering the basic principles of inheritance through his experiments with pea plants.

Option 4 states that genetics is the study of transmission of characters to the progeny from the parents and it is unrelated to evolution. This statement is incorrect. Genetics is indeed the study of transmission of traits from parents to offspring, but it is also closely related to the field of evolution. Genetics provides the mechanisms by which traits are inherited and can be passed on to future generations, which is an important aspect of understanding how evolution occurs.

In conclusion, option 4 is the correct answer as it contains an incorrect statement. Genetics is indeed related to evolution.