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: Calculate probability of first - pick

The probability of choosing an advanced book first. There are 3 advanced books out of 11 total books. So the probability $P_1=\frac{3}{11}$.

Step2: Calculate probability of second - pick

The probability of choosing a beginner book second. There are 2 beginner books out of 11 total books. Since the book is replaced, the probability $P_2 = \frac{2}{11}$.

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 $P = P_1\times P_2=\frac{3}{11}\times\frac{2}{11}=\frac{6}{121}$.

Answer:

$\frac{6}{121}$