A certain record collection consists of 10 records of chamber music, 15 records
ID: 3172339 • Letter: A
Question
A certain record collection consists of 10 records of chamber music, 15 records of vocal music, and 20 records of symphonic music. Find the number of ways 2 records may be selected from each of the 3 groups of records. Suppose that 3 of the chamber music records, 4 of the vocal music records, and 7 of the symphonic music records consist of compositions by Mozart. What, then, is the probability that a random selection of 2 records from each of the 3 groups will result in 6 records of compositions by Mozart? What is the probability that a random selection of 2 records from each of the 3 groups will result in no compositions by Mozart?Explanation / Answer
Record collection consists
10 Chamber music records
15 Vocal music records
20 symphonic music
(A)
If two records are selected from each of the group, 2 Chamber music can be selected in 10C2 ways, 2 Vocal music can be selected in 15C2 ways and 2 symphonic music can be selected in 20C2 ways
Hence total possible combinations are 10C2 * 15C2 * 20C2 = 897750
(B)
Composition by Mozat, 3 Chamber music, 4 vocal music and 7 symphonic music
Probability of selecting 2 chamber music by Mozat = 3C2/10C2 = 0.0667
Probability of selecting 2 vocal music by Mozat = 4C2/15C2 = 0.0571
Probability of selecting 2 symphonic music by Mozat = 7C2/20C2 = 0.1105
Hence required probability = 0.0667 * 0.0571 * 0.1105 = 0.00042
(C)
Probability of selecting 2 chamber music not by Mozat = 7C2/10C2 = 0.4667
Probability of selecting 2 vocal music not by Mozat = 11C2/15C2 = 0.5238
Probability of selecting 2 symphonic music not by Mozat = 13C2/20C2 = 0.4105
Hence required probability = 0.4667 * 0.5238 * 0.4105 = 0.1004
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