document.write( "Question 1134972: Assume that you randomly pick one of the bowls: X, Y, or Z. You then randomly draw one ball out of the selected bowl and note its color. The bowls contain the following colored balls: \r
\n" ); document.write( "\n" ); document.write( "Bowl X: 2 red, 1 white, and 2 blue.
\n" ); document.write( "Bowl Y: 1 red, 3 white, and 4 blue.
\n" ); document.write( "Bowl Z: 2 red, 3 white, and 2 blue.
\n" ); document.write( "(1) If the ball is blue, what is the probability that it was drawn from bowl X?
\n" ); document.write( "(2) If the ball is either blue or white, what is the probability that it was drawn from bowl Y? \n" ); document.write( "
Algebra.Com's Answer #752490 by greenestamps(13216)\"\" \"About 
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\n" ); document.write( "(1) If the ball is blue, what is the probability that it was drawn from bowl X? That probability is
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document.write( "  P((blue) AND (drawn from X))\r\n" );
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document.write( "          P(blue)
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document.write( "P((blue) AND (drawn from X)) = (1/3)(3/6) = 1/6    A  (equal probability of selecting any of the 3 bowls; 3 of the 6 balls in X are blue)\r\n" );
document.write( "P((blue) AND (drawn from Y)) = (1/3)(4/8) = 1/6    B  (equal probability of selecting any of the 3 bowls; 4 of the 8 balls in Y are blue)  \r\n" );
document.write( "P((blue) AND (drawn from Z)) = (1/3)(2/7) = 2/21   C  (equal probability of selecting any of the 3 bowls; 2 of the 7 balls in Z are blue)
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document.write( "P(blue) = 1/6 + 1/6 + 2/21 = (7+7+4)/42 = 18/42 = 3/7   D  (sum of A, B, and C)
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document.write( "P(blue AND drawn from X, given blue) = (1/6)/(3/7) = (1/6)*(7/3) = 7/18   (A/D)

\n" ); document.write( "(2) If the ball is either blue or white, what is the probability that it was drawn from bowl Y?

\n" ); document.write( "Exactly the same kind of problem; you can solve it using the same method.
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document.write( "P((blue OR white) AND (drawn from X)) = A\r\n" );
document.write( "P((blue OR white) AND (drawn from Y)) = B\r\n" );
document.write( "P((blue OR white) AND (drawn from Z)) = C
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document.write( "P(blue OR white) = D = A+B+C
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document.write( "P(blue OR white AND drawn from Y, given blue or white) = B/D
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