A spinner has 12 congruent sections. Sarah will spin the arrow on the spinner twice. What is the probability that the arrow will land on a WHITE (unshaded) section of the spinner on both spins?
To find the probability that the arrow will land on a WHITE section of the spinner on both spins, we need to determine the probability for each spin and then multiply them together.
Given that there are 12 congruent sections on the spinner, and we want to land on a WHITE section, we need to determine the total number of WHITE sections.
Assuming the spinner is equally divided, let's say there are 6 WHITE sections. Therefore, the probability of landing on a WHITE section on the first spin is 6/12, which simplifies to 1/2.
Since each spin is independent, the probability of landing on a WHITE section on the second spin is also 1/2.
To find the probability of both events happening, we multiply the probabilities together:
(1/2) * (1/2) = 1/4
Therefore, the probability that the arrow will land on a WHITE section on both spins is 1/4.
To find the probability that the arrow will land on a white section of the spinner on both spins, we need to determine the number of favorable outcomes (the arrow landing on a white section) and the total number of possible outcomes.
Given that the spinner has 12 congruent sections, we know that there are 12 possible outcomes for each spin. Since the spinner is symmetrical, we can assume that the probability of landing on a white section is the same for each spin.
Now, to calculate the probability of landing on a white section on the first spin, we divide the number of white sections (let's say there are w white sections) by the total number of sections (12 in this case): P(white on first spin) = w/12.
Similarly, for the second spin, the probability of landing on a white section is also w/12: P(white on second spin) = w/12.
Since the two spins are independent events, we can multiply the probabilities together to find the overall probability of both events occurring: P(white on first spin) × P(white on second spin) = (w/12) × (w/12).
Therefore, the probability that the arrow will land on a white section of the spinner on both spins is (w/12) × (w/12).
wondering the area of white as compared to non-white?
Take the probability of each one (1/12 and 1/12), and multiply both of the fractions together. That will give you the probability.
Answer: 1/24
Those kind of questions are called compound events. It's where you just have to take the probability of each "situation" and multiply them together. Though this answer is too late, I hope you understand the material. ;)