document.write( "Question 1115761: . A company has three machines A, B and C which all produce the same two parts, X and Y. of all the parts produced, machine A produces 60%, machine B produces 30%, and machine C produces the rest. 40% of the parts made by machine A are part X, 50% of the parts made by machine B are part X, and 70% of the parts made by machine C are part X. A part produced by this company is randomly sampled and is determined to be an X part. With the knowledge that it is an X part, find the probabilities that the part came from machine A, B or C. \n" ); document.write( "
Algebra.Com's Answer #730593 by ikleyn(52778)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( " \r\n" ); document.write( "Let aX = the number of parts X produced by machine A;\r\n" ); document.write( "\r\n" ); document.write( " aY = the number of parts Y produced by machine A;\r\n" ); document.write( "\r\n" ); document.write( " bX = the number of parts X produced by machine B;\r\n" ); document.write( "\r\n" ); document.write( " bY = the number of parts Y produced by machine B;\r\n" ); document.write( "\r\n" ); document.write( " cX = the number of parts X produced by machine C;\r\n" ); document.write( "\r\n" ); document.write( " cY = the number of parts Y produced by machine C.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Let P = aX + aY + bX + bY + cX + cY is the FULL NUMBER of all produced Parts. \r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Then the probability that the part X came from machine A is equal to\r \n" ); document.write( "\n" ); document.write( "Answer. The probability that the part X came from machine A = 0.5217 = 52.17%.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |