Question

nico owns 11 instructional piano books. two are beginner books, six are intermediate books, and three are advanced books.
if two books are randomly chosen from the collection, one at a time, and replaced after each pick, what is the probability that he first chooses an advanced book and then chooses a beginner book?
\\(\frac{5}{121}\\)
\\(\frac{6}{121}\\)
\\(\frac{5}{11}\\)
\\(\frac{6}{11}\\)

Explanation:

Step1: Find probability of advanced book

There are 3 advanced books out of 11 total. So \( P(\text{advanced}) = \frac{3}{11} \).

Step2: Find probability of beginner book

There are 2 beginner books out of 11 total. Since we replace, \( P(\text{beginner}) = \frac{2}{11} \).

Step3: Multiply the probabilities

For independent events (with replacement), multiply the probabilities: \( \frac{3}{11} \times \frac{2}{11} = \frac{6}{121} \).

Answer:

\(\frac{6}{121}\) (corresponding to the option with this value)