Question

a music collection includes 18 rock cds, 13 country cds, 6 classical cds, and 5 hip hop cds.
a. what is the probability that a cd randomly selected from the collection is a classical cd?
b. what is the probability that a cd randomly selected from the collection is not a classical cd?
a. the probability is \\(\frac{1}{7}\\) that a randomly selected cd is a classical cd. (simplify your answer.)
b. the probability is \\(square\\) that a randomly selected cd is not a classical cd. (simplify your answer.)

Explanation:

Step1: Calculate total number of CDs

First, we find the total number of CDs in the collection. We add the number of each type of CD: rock (18), country (13), classical (6), and hip - hop (5). So, the total number of CDs \(n = 18+13 + 6+5=42\).

Step2: Calculate number of non - classical CDs

The number of classical CDs is 6. So, the number of non - classical CDs is the total number of CDs minus the number of classical CDs. That is \(42 - 6=36\).

Step3: Calculate the probability of non - classical CD

The probability of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). For the event of selecting a non - classical CD, the number of favorable outcomes is 36 and the total number of outcomes is 42. We simplify the fraction \(\frac{36}{42}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6. \(\frac{36\div6}{42\div6}=\frac{6}{7}\).

Answer:

\(\frac{6}{7}\)