document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172368>Question 1172368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white<BR>\n" );
document.write( "balls and 5 black balls. One ball is drawn from the first bag and placed unseen in<BR>\n" );
document.write( "the second bag. What is the probability that a ball now drawn from the second<BR>\n" );
document.write( "bag is black? </SPAN>\n" );
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document.write( "There are two cases to analyze: the ball drawn from the first bag can be either white or black.<br><BR>\n" );
document.write( "Case 1: first ball white<br><BR>\n" );
document.write( "P(white from first bag) = 4/7.<BR>\n" );
document.write( "There are now 4 white and 5 black in the second bag; P(black from second bag) = 5/9.<BR>\n" );
document.write( "P(white then black) = (4/7)(5/9) = 20/63.<br><BR>\n" );
document.write( "Case 2: first ball black<br><BR>\n" );
document.write( "P(black from first bag) = 3/7.<BR>\n" );
document.write( "There are now 3 white and 6 black in the second bag; P(black from second bag) = 6/9.<BR>\n" );
document.write( "P(black then black) = (3/7)(6/9) 18/63.<br><BR>\n" );
document.write( "ANSWER: P black from second bag = 20/63+18/63 = 38/63.<br><BR>\n" );
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