Final answer:
The probability of any one specific applicant not being selected for any of the three positions is 8/27, calculated by raising (2/3), the probability of not being selected for a single position, to the power of 3.
Step-by-step explanation:
The question pertains to the field of probability and asks about the chance of not selecting any one applicant when 9 applicants are competing for 3 positions. To calculate this probability, one must understand that the question implies the probability of any specific applicant not being chosen.
Since there are 3 positions available, the probability that a specific individual is selected for one position is 3/9 or 1/3, assuming each applicant has an equal chance. Therefore, the probability that this specific applicant is not selected for a single position is 1 - 1/3, which simplifies to 2/3. Since the positions are filled independently, to find the probability that the individual is not selected for any position, we raise (2/3) to the power of 3. This gives us (2/3)^3 = 8/27, representing the probability that a specific individual is not selected for any of the three positions.