Ex3soln - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1306 INTRODUCTORY STATISTICS (Sem 1 2008 / 2009) EXAMPLE CLASS 3 ANSWERS 1. Let ST = Static Electricity M = Malfunctioning equipment C = Carelessness SB = Sabotage E = Explosion 0.25 ST E 0.30 0.20 M E 0.30 0.25 C 0.40 E 0.15 SB 0.75 E 0.3 x 0.25 P(ST | E) = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ (0.3 x 0.25) + (0.3 x 0.2) + (0.4 x 0.25) + (0.15 x 0.75) 0.075 = ⎯⎯⎯⎯ 0.3475 = 0.2158
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0.3 x 0.2 P(M | E) = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ (0.3 x 0.25) + (0.3 x 0.2) + (0.4 x 0.25) + (0.15 x 0.75) 0.06 = ⎯⎯⎯⎯ 0.3475 = 0.1727 0.4 x 0.25 P(C | E) = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ (0.3 x 0.25) + (0.3 x 0.2) + (0.4 x 0.25) + (0.15 x 0.75) 0.1 = ⎯⎯⎯⎯ 0.3475 = 0.2878 0.15 x 0.75 P(SB | E) = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ (0.3 x 0.25) + (0.3 x 0.2) + (0.4 x 0.25) + (0.15 x 0.75) 0.1125 = ⎯⎯⎯⎯ 0.3475 = 0.3237 The MOST likely cause of the explosion is SABOTAGE The LEAST likely cause is malfunctioning equipment.
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2. ⎯⎯→ 4 marbles are drawn at random
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This note was uploaded on 09/06/2010 for the course STAT STAT1306 taught by Professor Prof during the Fall '08 term at HKU.

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Ex3soln - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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