Question

algebra i b-cr
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 P(advanced book)

Total books = 11, advanced books = 3.
$P(\text{advanced}) = \frac{3}{11}$

Step2: Find P(beginner book)

Beginner books = 2, total books remain 11 (with replacement).
$P(\text{beginner}) = \frac{2}{11}$

Step3: Multiply the two probabilities

Since picks are independent (with replacement), multiply the probabilities.
$P(\text{advanced then beginner}) = \frac{3}{11} \times \frac{2}{11} = \frac{6}{121}$

Answer:

$\boldsymbol{\frac{6}{121}}$ (Option: $\boldsymbol{\frac{6}{121}}$)