document.write( "Question 1163319: You are given two urns, each containing a collection of coloured balls. Urn 1 contains three white and two blue balls. Urn 2 contains four white and three blue balls. A ball is drawn at random from urn 1 and put into urn 2. A ball is then picked a random from Urn 2.
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Algebra.Com's Answer #787381 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "You are given two urns, each containing a collection of coloured balls.
\n" ); document.write( "Urn 1 contains three white and two blue balls.
\n" ); document.write( "Urn 2 contains four white and three blue balls.
\n" ); document.write( "A ball is drawn at random from urn 1 and put into urn 2.
\n" ); document.write( "A ball is then picked a random from Urn 2.
\n" ); document.write( "What is the probability that the ball picked is white? Assume balls picked from an urn are equally likely to be any of the balls present.
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document.write( "(1)  Analyzing the first step, when we draw the ball from Urn 1 and put it into Urn 2:\r\n" );
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document.write( "         After the first step, we draw the white ball from Urn 1 with the probability of   =  and put it into Urn 2.\r\n" );
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document.write( "         So, with the probability    we get the content (5white,3blue) in the Urn 2 at this step.\r\n" );
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document.write( "         Alternatively, with the complement probability    we get the content (4white,4blue) in Urn 2 at this step.\r\n" );
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document.write( "(2)  Analyzing the second step, when we draw a ball from Urn 2, we have two respective alternatives\r\n" );
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document.write( "         we draw a white ball from Urn 2  (5w,3b)  with the probability   = ,  or\r\n" );
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document.write( "         we draw a white ball from Urn 2  (4w,4b)  with the probability   = .\r\n" );
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document.write( "(3)  Now the probability to have finally a white ball from Urn 2 is\r\n" );
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document.write( "         P =  +  =  +  = .    ANSWER\r\n" );
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