Final answer:
The probability that the spinner lands on a shaded section for two consecutive spins is the square of the probability of landing on a shaded section in one spin, which requires the number of shaded sections.
Step-by-step explanation:
The subject of this question is probability. The student must calculate the probability that the arrow lands on a shaded section of the spinner in two consecutive spins. Since the spinner has 12 congruent sections, we need to know the number of shaded sections to determine the probability of landing on a shaded section in one spin.
Let's assume the number of shaded sections is n. The probability of landing on a shaded section in one spin would be P(shaded) = n/12. Since each spin is independent, the probability that the arrow lands on a shaded section on both spins would be the product of the probabilities of each individual spin, which is P(shaded on first spin) × P(shaded on second spin).
If n is the number of shaded sections, then the probability of the arrow landing on a shaded section for each spin is n/12. Therefore, the probability of landing on a shaded section on both spins would be:
P(both spins shaded) = (n/12) × (n/12) = (n^2)/(12^2).
To give a specific answer, the exact number of shaded sections (n) needs to be known, which is not provided in the question.