To determine the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number, let's follow these steps:
1. Identify Total Marbles:
- There are 11 marbles in total.
2. Determine the Number of Shaded Marbles:
- Assume there are 6 shaded marbles.
3. Calculate the Probability of Choosing a Shaded Marble First:
- Since there are 11 total marbles and 6 of them are shaded, the probability of choosing a shaded marble first is:
[tex]\[ P(\text{shaded}) = \frac{6}{11} \][/tex]
4. Determine the Number of Marbles Labeled with Odd Numbers:
- Assume there are 5 marbles labeled with odd numbers.
5. Calculate the Probability of Choosing a Marble Labeled with an Odd Number Second:
- The probability of choosing a marble labeled with an odd number, since the events are independent and the marble is replaced, is:
[tex]\[ P(\text{odd number}) = \frac{5}{11} \][/tex]
6. Determine the Combined Probability:
- Since the selections are independent events, the combined probability of both events happening is the product of the two individual probabilities:
[tex]\[ P(\text{shaded and odd}) = P(\text{shaded}) \times P(\text{odd number}) = \frac{6}{11} \times \frac{5}{11} \][/tex]
7. Calculate the Combined Probability:
[tex]\[ P(\text{shaded and odd}) = \frac{6}{11} \times \frac{5}{11} = \frac{30}{121} \][/tex]
Therefore, the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number is:
[tex]\[ \boxed{\frac{30}{121}} \][/tex]
Since none of the provided multiple-choice options directly match this answer, it would be prudent to check that the assumptions (such as the number of shaded and odd-labeled marbles) align correctly with the actual scenario or question context.
