To determine the probability that the color of the marble matches the color on which the spinner lands, let's analyze the situation step-by-step:
1. Spinner Sections:
- The spinner has 4 sections: orange, black, purple, and white.
2. Marble Colors:
- The marbles in the bag come in 3 colors: orange, black, and purple.
- There is no white marble in the bag.
3. Possible Scenarios:
- When the spinner is spun, it can land on any one of its 4 sections (orange, black, purple, white) with equal probability.
- When Renee picks a marble from the bag, there are only 3 possible matching colors (orange, black, purple) that she can pick. There is no white marble, so if the spinner lands on white, it is impossible to match it with a marble.
4. Calculating the Probability:
- There are 3 favorable outcomes where the marble color can match the spinner color (orange, black, purple).
- There are a total of 4 possible outcomes for the spinner (orange, black, purple, white).
5. Finding the Probability:
- The probability is the number of favorable outcomes divided by the total number of possible outcomes on the spinner.
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes on the spinner}} \][/tex]
[tex]\[ \text{Probability} = \frac{3}{4} \][/tex]
The probability that the color of the marble matches the color on which the spinner lands is [tex]\(\frac{3}{4}\)[/tex] or 0.75.
Thus, the correct answer is:
[tex]\[ \boxed{\frac{3}{4}} \][/tex]
