The Recording Industry Association of America provides data on the best-selling

Question

The Recording Industry Association of America provides data on the best-selling albums of all times. As of January, 2008, the top six best-selling albums of all times (U.S. sales only), are by the artists the Eagles (E), Michael Jackson (M), Pink Floyd (P), Led Zepplin (L), AC/DC (A), and billy Joel (B). a. list the 15 possible samples without replacement of two artisis that can be selected from the six. For brevity, use the intial 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?

Explanation / Answer

a) As 2 have to be selected from the 6 artists given, this could be done in 6c2 = 15 ways. These are:

S = { EM, EP, EL, EA, EB, MP, ML, MA, MB, PL, PA, PB, LA, LB, AB }

b) The procedure we followed for taking a sample random sample of 2 artists from the 6 could be random sampling where we first select 1 out of the 6 available and then we selected the other from the 5 available.

c) If a simple random sampling is done to select the 2 artists, then each of the events mentioned in a) would have equal probability of occurence. Therefore the probability of selecting P and A would be equal to the probability of selecting M and E and both would be equal to 1/15 = 0.0667

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