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Unformatted text preview: (1) A certain type of CD players is produced by two factories (CD players produced by both factories look identical). Factory A produces 40 % of all players and factory B produces 60 % of all players. 1% of all players produced at factory A are defective and 3% of all players produced at factory B are defective. A customer buys a random CD player. (a) Find the probability that the player is defective. (b) Find the conditional probability that the player is pro- duced by factory B given that the player is defective. Solution. Let A,B denote the events that the player is produced by factory A, respectively B. Let D be the event that the player is defective. By law of total probability P ( D ) = P ( A ) P ( D | A )+ P ( B ) P ( D | B ) = 0 . 4 × . 01+0 . 6 × . 03 = 0 . 022 . P ( B | D ) = P ( BD ) /P ( D ) = 0 . 6 × . 03 / . 022 = 9 / 11 . (2) Let X have a density equal to cx if x ∈ [0 , 1] and equal to 0 elsewhere ( c is an unknown constant)....
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This note was uploaded on 02/09/2012 for the course STAT 410 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08