To determine the probability that a marble chosen at random is either shaded or labeled with a multiple of 3, follow these steps:
1. Total number of marbles in the bag: There are 11 marbles in the bag.
2. Number of shaded marbles: There are 2 shaded marbles in the bag.
3. Identify marbles labeled with a multiple of 3: We need to list the marbles that have labels that are multiples of 3.
- Multiples of 3 within the range of 1 to 11 are: 3, 6, and 9.
- So, there are 3 marbles labeled with numbers that are multiples of 3.
4. Calculate the number of marbles that are either shaded or labeled with a multiple of 3:
- Since shaded and labeled with multiples of 3 are independent, we simply add the number of shaded marbles and the number of marbles labeled with multiples of 3.
- Number of shaded marbles: 2
- Number of marbles labeled with multiples of 3: 3
- Therefore, the total number of marbles that are either shaded or labeled with a multiple of 3 = 2 (shaded) + 3 (multiples of 3) = 5
5. Determine the probability:
- Probability is the number of favorable outcomes divided by the total number of possible outcomes.
- The number of marbles that meet the criteria (shaded or labeled with a multiple of 3) is 5.
- Total number of marbles is 11.
- Therefore, the probability = [tex]\(\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{11}\)[/tex].
So, the probability that a randomly chosen marble is either shaded or labeled with a multiple of 3 is [tex]\(\frac{5}{11}\)[/tex]. This corresponds to answer (C) in the provided choices.
