Final answer:
The student's question pertains to blood type proportions, and the probabilities related to type B blood in a population. Approximately 1 in 9 people have type B blood, and using a Poisson distribution, we can calculate the likelihood of different scenarios occurring within a given set of 100 people. Probabilities regarding the sequence until a type B individual is found can be assessed with negative binomial distributions.
Step-by-step explanation:
The question deals with the proportions of different blood types in a population and associated probabilities. Blood type distinctions are based on the presence of certain antigens on the surface of red blood cells (RBCs). There are four main blood types: A, B, AB, and O. Blood type A has only the A antigen, blood type B has only the B antigen, blood type AB has both, and blood type O has neither.
According to the American Red Cross, about 1 in 9 people (11.1%) in the U.S. have type B blood. When considering a group of 100 people, on average, we would expect 11 of them to have type B blood. Since the arrival of individuals with a particular blood type can be modeled by a Poisson distribution, the probability of observing more than 10 people with type B blood in a group of 100 can be calculated using the Poisson probability function with a mean (λ) of 11.1.
Furthermore, the probability of more than 20 people arriving before finding someone with type B blood can be calculated using the concepts of geometric or negative binomial distributions, since this scenario describes a sequence of trials until a success (finding a type B individual) occurs.
People with blood type O have neither A nor B antigens on their RBCs and produce antibodies against both A and B antigens. On the other hand, those with type B blood have B antigens and do not have the A antigen, which distinguishes them from type O.
The variation in blood types and antigens is important for many medical applications, including blood transfusions and understanding genetics related to blood types. For example, when two individuals with AB blood type have children, the phenotype ratio for their children's blood types is 1A:2AB:1B, which is indicative of codominance, where both A and B alleles express their traits fully.