document.write( "Question 92278: One urn contains 3 read and 7 white marbles. A second urn contains 2 red and 8 white marbles. One urn is selected and a ball drawn. The probability of selecting the first urn is 0.4 and the probability of selecting the second is 0.6. If a white ball is drawn, find the probability it came from the second urn. \n" ); document.write( "
Algebra.Com's Answer #67191 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
One urn contains 3 read and 7 white marbles. A second urn contains 2 red and 8 white marbles. One urn is selected and a ball drawn. The probability of selecting the first urn is 0.4 and the probability of selecting the second is 0.6. If a white ball is drawn, find the probability it came from the second urn.
\n" ); document.write( "---------
\n" ); document.write( "P(2nd urn|white) = P(2nd and white)/P(w)
\n" ); document.write( "-------------
\n" ); document.write( "But P(2nd and white) = 8/20 = 2/5 = 0.4
\n" ); document.write( "---------
\n" ); document.write( "And P(w) = P(w |1st urn)+P(w |2nd urn)
\n" ); document.write( "=P(w AND 1st)/P(1st)+P(w AND 2nd)/P(2nd)
\n" ); document.write( "= (7/20)/(8/20 + (8/20)/(12/20)
\n" ); document.write( "= (7/8) + (2/3)
\n" ); document.write( "= 37/24
\n" ); document.write( "---------------
\n" ); document.write( "Final: P(2nd urn |white) = 0.4/(37/24) = 0.259...
\n" ); document.write( "===========
\n" ); document.write( "If you have another answer I would like to see it.
\n" ); document.write( "Why? Probability problems are always tricky.
\n" ); document.write( "=============
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H
\n" ); document.write( "
\n" ); document.write( "
\n" );