AIDS, which stands for Acquired Immune Deficiency Syndrome, is caused by the Human Immunodeficiency Virus (HIV). The virus is primarily transmitted through:

I. Sexual intercourse: This is one of the most common ways HIV is transmitted, especially through unprotected sex. It is correct.

II. Blood transfusion: HIV can also be transmitted through the transfusion of contaminated blood. Thus, this option is correct.

III. Mosquitoes and other blood-sucking insects: There is no evidence to suggest that AIDS can be transmitted through mosquitoes or other blood-sucking insects. An infected mosquito does not inject HIV-infected blood into the next person it bites. Therefore, this statement is incorrect

IV. Across the placenta: HIV can also be transmitted from an HIV-positive mother to her child during pregnancy, childbirth, or breastfeeding. This is referred to as mother-to-child transmission or perinatal transmission. Hence, this option is correct.

The correct answer, thus, is option 2: I, II, and IV are the correct statements, as they confirm how AIDS is transmitted.