Final answer:
The theorem of total probability suggests that to find the probability of event A, you sum the probabilities of A given each event Ei, typically also including the probability of Ei itself if venturing beyond a simple conditional probability.
Step-by-step explanation:
The theorem of total probability is a fundamental rule in probability theory that relates marginal probabilities to conditional probabilities. When we refer to the event A as the event of selecting a color-blind person and Ei as the event of selecting a person (from different groups or categories, for example), then the law of total probability states that:
P(A) = Σ P(A|Ei)P(Ei)
Given a list of mutually exclusive and collectively exhaustive events Ei, the probability of A can be found by summing up the probabilities of A given each event Ei multiplied by the probability of Ei. Therefore, the correct answer to the question "What is P(A)?" is:
a) P(A) = Σ P(A|Ei) (correct if considering the sum over i includes the probability of Ei)
This expression summarizes the total probability of event A happening over all the possible scenarios provided by the different Ei events.