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. 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?\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. 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?\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 total number of books is $2 + 6+3=11$. The number of advanced books is 3. The probability of choosing an advanced book on the first - pick, $P(A)=\frac{3}{11}$ since probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Calculate probability of choosing beginner book

Since the book is replaced, the total number of books remains 11. The number of beginner books is 2. The probability of choosing a beginner book on the second - pick, $P(B)=\frac{2}{11}$.

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:

$\frac{6}{121}$