Final answer:
To calculate the probability that the spinner will land on a shaded section twice, multiply the probability of one spin landing on shaded section by itself. If 3 out of 12 sections are shaded, the probability for two spins is (1/4) × (1/4) = 1/16, or around 6.25%.
Step-by-step explanation:
The student's question is about calculating the probability that a spinner will land on a shaded section twice when spun two times. Since each section has an equal area, if the spinner is divided into 12 congruent sections, the probability of landing on a shaded section in one spin would be the number of shaded sections divided by 12.
If, for example, there are 3 shaded sections, the probability of landing on a shaded section in one spin would be 3/12 or 1/4.
Since each spin is independent, the probability of landing on a shaded section on both spins would be calculated by multiplying the probabilities from each spin: P(shaded on first spin) × P(shaded on second spin). Therefore, the probability would be (1/4) × (1/4) = 1/16.
To get the final answer, you convert 1/16 to a decimal or a percentage. Hence, the probability that the arrow will land on a shaded section of the spinner on both spins is 1/16 or about 6.25%.