Best-Selling Albums. The Recording Industry Association of America provides data on the best-selling albums of all time. As of May 28, 2013, the top six best-selling albums of all time (U.S. sales only), are by the artists the Eagles (E), Michael Jackson (M), Pink Floyd (P), Led Zeppelin (L), AC/DC (A), and Billy Joel (B).

(a). List the 15 possible samples (without replacement) of two artists that can be selected from the six. For brevity, use the initial provided.

(b). Describe a procedure for taking a simple random sample of two artists from the six.

(c). If a simple random sampling procedure is used to obtain two artists, what are the chances of selecting P and A? M and E?

The given information is:

The Recording Industry Association of America provides data on the best-selling albums of all time. As of May 28, 2013, the top six best-selling albums of all time (U.S. sales only), are by the artists the Eagles (E), Michael Jackson (M), Pink Floyd (P), Led Zeppelin (L), AC/DC (A), and Billy Joel (B).

The 15 possible samples (without replacement) of two artists that can be selected from the six best-selling albums of all time:

(E, M), (E, P), (E, L), (E, A), (E, B), (M, P), (M, L), (M, A), (M, B), (P, L), (P, A), (P, B), (L, A), (L, B), (A, B)

Procedure:

Using Random Table, two artists out of the given six can be chosen at random.

The artists are listed in order from 1 to 6.

From the Random Table, a line number and column number are chosen at random, and two numbers from 1 to 6 are chosen by moving down in the selected column.

As a result, two artists are chosen at random from a pool of six.

Total samples are 15.

There is only one outcome of selecting Pand A.

Therefore, the Chance of selecting Pand A:

$$\begin{gathered} =\frac{1}{15} \\ =0.067 \end{gathered}$$

Similarly, there is only one outcome of selecting M and E.

Therefore, the Chance of selecting M and E is:

$$\begin{gathered} =\frac{1}{15} \\ =0.067 \end{gathered}$$