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Econ319_08S_01sol

# Econ319_08S_01sol - Econ 319 Spring 2008 TA Seung Han Yoo...

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Econ 319 Spring 2008 TA: Seung Han Yoo Solution to Problem Set 1 1. (#1.27) 26 ° 25 ° 24 ° 23 ° 22 26 5 2. (#1.30) a. ( 55 25 ) ° 2 ( 60 30 ) = 0 : 05 . b. ( 55 26 )( 5 4 ) ° 2 ( 60 30 ) = 0 : 3 . c. ( 55 26 ) ° 2 ( 60 30 ) = 0 : 06 . 3. (#1.38) a. ° 6 3 ± = 20 . b. ° 9 6 ±° 6 3 ± = 1680 . 4. (#1.42) ° 11 4 ±° 7 3 ±° 4 3 ± = 46 ; 200 . 5. (#1.48) a. Let W 2 denote the event that the second ball drawn is white, W 1 denote the event that the °rst ball drawn is white and R 1 denote the event that the °rst ball drawn is red. P ( W 2 ) = P ( W 2 \ W 1 ) + P ( W 2 \ R 1 ) = P ( W 2 j W 1 ) P ( W 1 ) + P ( W 2 j R 1 ) P ( R 1 ) = 3 6 ° 2 5 + 2 6 ° 3 5 = 2 5 . b. P ( W 1 j W 2 ) = P ( W 2 \ W 1 ) P ( W 2 ) = 1 = 5 2 = 5 = 1 2 . 6. (#1.57) The event that given that a silver coin is found in a cabinet, the other drawer in the 1

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cabinet contains a silver coin is the same as the event that given that a silver coin is found in a cabinet, the cabinet is B . P ( B j S ) = P ( B \ S ) P ( S ) = P ( S j B ) P ( B ) P ( S j A ) P ( A )+ P ( S j B ) P ( B )+ P ( S j C ) P ( C ) = 1 = 3 1 = 3+1 = 2 ° 1 = 3 = 2 3 . 7. (#1.60) a. P ( D ) = P ( D \ S 1 ) + P ( D \ S 2 ) + P ( D \ S 3 ) = P ( D j S 1 ) P ( S 1 )+ P ( D j S 2 ) P ( S 2 )+ P ( D j S 3 ) P ( S 3 ) = 1 3 [0 : 01 + 0 : 02 + 0 : 05] = 0 : 0266 .
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