To find the probability that Nico first chooses an advanced book and then a beginner book with replacement, we can follow these detailed steps:
1. Total Number of Books:
Nico has 11 books in total.
2. Advanced Books:
Nico has 3 advanced books out of the 11.
3. Beginner Books:
Nico has 2 beginner books out of the 11.
4. Probability of Picking an Advanced Book First:
The probability of picking an advanced book in the first draw is found by dividing the number of advanced books by the total number of books:
[tex]\[
\text{Probability of advanced book first} = \frac{3}{11}
\][/tex]
5. Probability of Picking a Beginner Book Second:
Since the books are replaced after each pick, the total number of books remains the same for the second draw. The probability of picking a beginner book in the second draw is:
[tex]\[
\text{Probability of beginner book second} = \frac{2}{11}
\][/tex]
6. Combined Probability:
The combined probability of both events happening (picking an advanced book first and then picking a beginner book) is the product of their individual probabilities:
[tex]\[
\text{Combined probability} = \left( \frac{3}{11} \right) \times \left( \frac{2}{11} \right) = \frac{3 \times 2}{11 \times 11} = \frac{6}{121}
\][/tex]
Thus, the probability that Nico picks an advanced book first and a beginner book second with replacement is:
[tex]\[
\boxed{\frac{6}{121}}
\][/tex]
