hw problem set 2 - Answer Key to Homework#2 Econ 41 Winter...

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Answer Key to Homework #2 Econ 41 Winter 2008 Amy Brown University of California, Los Angeles 4.126 Happy Unhappy Psych 80 20 100 Comm 115 35 150 195 55 250 a. i. The probability that the student is happy with the major is P ( H ) = 195 250 = 0 : 78 . ii. The probability that the student is a psych major is P ( P ) = 100 250 = 0 : 40 . iii. The probability that the student is a communications major given that he is happy is P ( C j H ) = 115 195 = 0 : 59 . iv. The probability that the student is unhappy given that she is a psychology student is P ( U j P ) = 20 100 = 0 : 20 . v. The probability that the student is a psychology major and happy is P ( P \ H ) = P ( P ) P ( H j P ) = 100 250 80 100 = 0 : 32 . vi. The probability that a student is a communications major or unhappy is P ( C [ U ) = P ( C ) + P ( U ) ° P ( C \ U ) = 150 250 + 55 250 ° 35 250 = 0 : 68 . b. P ( P ) = 100 250 = 0 : 40 and P ( P j H ) = 80 195 = 0 : 4103 . Since these two proba- bilities are not equal, the events "P" and "H" are dependent. The events "P" and "H" are not mutually exclusive because they can occur together; i.e., P ( P \ H ) 6 = 0 . 4.131 Let A be the °rst employee selected has con°dence in senior management, B that the °rst employee selected does not have con°dence in senior man- agement, C that the second employee selected has con°dence in senior management and D that the second employee does not have con°dence in senior management. Then the tree diagram is ° A P ( A ) = 0 : 51 B P ( B ) = 0 : 49 8 > > < > > : C j A P ( C j A ) = 0 : 51 P ( A \ C ) = 0 : 51 ± 0 : 51 = 0 : 26 D j A P ( D j A ) = 0 : 49 P ( A \ D ) = 0 : 51 ± 0 : 49 = 0 : 25 C j B P ( C j B ) = 0 : 51 P ( B \ C ) = 0 : 49 ± 0 : 51 = 0 : 25 D j B P ( D j B ) = 0 : 49 P ( B \ D ) = 0 : 49 ± 0 : 49 = 0 : 24 a. P ( A \ C ) = 0 : 26 1
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