Cilantro leaves are widely used in many world cuisines. While some people enjoy it, others claim that it has a soapy, pungent aroma. A recent study conducted on participants of European ancestry identified a genetic variant that is associated with soapy-taste detection. In the initial questionnaire, 1,994 respondents out of 14,604 reported that they thought cilantro tasted like soap. Suppose that participants are randomly selected one by one.

(a) What is the probability that the first soapy-taste detector is the third person selected?

(b) What is the probability that in a sample of ten people, no more than two are soapy-taste detectors?

(c) What is the probability that three soapy-taste detectors are identified from sampling ten people?

(d) What is the mean and standard deviation of the number of people that must be sampled if the goal is to identify four soapy-taste detectors?