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You are solving the probability that this transfusion can lead to a serious complication based on the mixing of blood types and Rh factors.

Blood consists of various types of cells submerged in plasma, containing protein molecules known as antigens and antibodies. Mixing blood with different antigens and antibodies can be highly dangerous. Antigens are found on the surface of red blood cells, while antibodies are present in the blood plasma. Danger arises when antigens and antibodies of incompatible types bind, leading to clumping and potential toxic reactions.

Consider a scenario of a blood transfusion involving red blood cells. There are four blood groups based on the presence of antigens and antibodies: - Blood group A: A antigens and B antibodies - Blood group B: B antigens and A antibodies - Blood group AB: A and B antigens, and no antibodies - Blood group O: No antigens, but both A and B antibodies

The percentage distribution of these blood types in the population is as follows: - O: 45% - A: 40% - B: 11% - AB: 4%

Additionally, there is another protein on the surface of red blood cells indicating the Rh factor. Individuals either carry this protein (Rh+) or do not (Rh-). The prevalence of Rh+ is approximately 85%, while Rh- is approximately 15%. It is critical to note that Rh+ individuals should not donate blood to Rh- individuals, but Rh- individuals can donate to anyone. Transfusions between Rh+ to Rh+ and Rh- to Rh- individuals are considered safe.

Now, suppose a red blood cell transfusion occurs between two randomly chosen individuals from the population, without checking their blood types or Rh factors

Determine the probability that this transfusion can lead to a serious complication based on the mixing of blood types and Rh factors.