To determine the probability that the color of the marble Renee picks from the bag matches the color on which the spinner lands, we need to consider the following:
1. Identify the possible outcomes for the spinner: The spinner has four sections, so each spin could result in one of four possible colors (Orange, Black, Purple, White).
2. Identify the possible outcomes for the marble: The marbles come in three colors (Orange, Black, Purple). This means there are three possible marble colors.
3. Determine the matching cases: We need to count the cases where the color on which the spinner lands matches the color of the marble picked from the bag. Since the spinner has sections marked Orange, Black, Purple, and White, and the bag has marbles of colors Orange, Black, and Purple, there are three sections where a match is possible (Orange, Black, Purple).
4. Calculate the probability: The probability of a match occurring is found by dividing the number of matching outcomes by the total number of possible outcomes for the spinner.
The total number of possible outcomes for the spinner is [tex]\(4\)[/tex] (since there are four sections). The number of favorable matching outcomes is [tex]\(3\)[/tex] (since only Orange, Black, and Purple can match the spinner results).
Therefore, the probability [tex]\(P\)[/tex] that the color of the marble matches the color on which the spinner lands is given by:
[tex]\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{4}
\][/tex]
Simplified, this fraction remains [tex]\(\frac{3}{4}\)[/tex], which in decimal form is [tex]\(0.75\)[/tex].
Among the given options:
A. [tex]\(\frac{1}{6}\)[/tex]
B. [tex]\(\frac{1}{4}\)[/tex]
C. [tex]\(\frac{1}{3}\)[/tex]
D. [tex]\(\frac{1}{2}\)[/tex]
None of these match our calculated probability [tex]\(\frac{3}{4}\)[/tex], so upon reviewing, it seems that none of the answer choices directly correspond to our result. However, if forced to choose the closest, [tex]\(\frac{3}{4}\)[/tex] is not represented accurately.
We should bring this inconsistency to the instructor's attention, expressing that there might be an error in the provided answer choices since [tex]\(\frac{3}{4}\)[/tex] is the correct calculated probability. The solution provides an accurate match of [tex]\(0.75\)[/tex] closest to [tex]\(\frac{3}{4}\)[/tex], not explicitly present in the given options.
