nico owns 11 instructional piano books. two are beginner books, six are intermediate books, and three are…

nico owns 11 instructional piano books. two are beginner books, six are intermediate books, and three are advanced books.\nif 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?\n$\frac{5}{121}$\n$\frac{6}{121}$\n$\frac{5}{11}$\n$\frac{6}{11}$

nico owns 11 instructional piano books. two are beginner books, six are intermediate books, and three are advanced books.\nif 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?\n$\frac{5}{121}$\n$\frac{6}{121}$\n$\frac{5}{11}$\n$\frac{6}{11}$

Answer

Explanation:

Step1: Calculate probability of choosing advanced book

The probability of choosing an advanced book on the first pick is the number of advanced books divided by the total number of books. There are 3 advanced books and 11 total books, so the probability $P(A)=\frac{3}{11}$.

Step2: Calculate probability of choosing beginner book

Since the book is replaced, the probability of choosing a beginner book on the second pick is the number of beginner books divided by the total number of books. There are 2 beginner books and 11 total books, so the probability $P(B)=\frac{2}{11}$.

Step3: Calculate combined probability

Since the two events are independent (because of replacement), the probability of both events occurring is the product of their individual probabilities. So $P = P(A)\times P(B)=\frac{3}{11}\times\frac{2}{11}=\frac{6}{121}$.

Answer:

$\frac{6}{121}$