Final answer:
The correct option is b. fourth person selected.
The probability that the first person selected who tried to quit smoking four or more times is either the second or the fourth person involves using the complement rule. For the second person, it is (1-p) * p, and for the fourth person, it is (1-p) * (1-p) * (1-p) * p, with p being 22% or 0.22.
Step-by-step explanation:
The question revolves around finding the probability that the first person selected, who tried to quit smoking four or more times, is the second person selected or the fourth person selected. To tackle the problem, we use the concept of probability and the complement rule. Assume that 'p' is the probability of the desired event (a person has tried to quit four or more times). According to the question, p = 22% or 0.22.
For part (a), the probability that the first person with the desired characteristic is the second person selected is (1-p) * p. This is because the first person must not have tried to quit four or more times (probability 1-p), and the second person must have tried (probability p).
For part (b), the probability that the first person with the desired characteristic is the fourth person selected involves three people not having the characteristic and then the fourth person having it: (1-p) * (1-p) * (1-p) * p. We calculate this by multiplying the probability of not having the characteristic (1-p) three times, and then the probability of having it (p) once.