document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120786>Question 1120786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three bags labelled P, Q and R contains red, blue and white balls respectively of equal sizes. The ratio of the balls in the bags are P:Q=2:1 and Q:R=4:5. All the balls are removed into a big bag and properly mixed together.<BR>\n" );
document.write( "(a) Find the probability of pick a red ball.<BR>\n" );
document.write( "(b) If two balls are picked at random one after the other with replacement, find the probability of picking:<BR>\n" );
document.write( "(i) a white ball and a blue ball<BR>\n" );
document.write( "(ii) a blue ball first and then a red ball.  </SPAN>\n" );
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document.write( "When given the ratio of P:Q and the ratio of Q:R, you can get a ratio of all three by making the value of Q in both ratios the same:<br><BR>\n" );
document.write( "P:Q = 2:1 and Q:R = 4:5  -->  P:Q = 8:4 and Q:R = 4:5<br><BR>\n" );
document.write( "Then P:Q:R = 8:4:5<br><BR>\n" );
document.write( "Now, given that ratio,<BR>\n" );
document.write( "let P = 8x<BR>\n" );
document.write( "let Q = 4x<BR>\n" );
document.write( "let R = 5x<br><BR>\n" );
document.write( "Then after all the balls are mixed together, 8/17 of them are red (P), 4/17 are blue (Q), and 5/17 are white (R).<br><BR>\n" );
document.write( "(a) The probability of picking a red ball is 8/17.<br><BR>\n" );
document.write( "(b)(i) To pick a white and a blue with replacement, you can pick either a white first and then a blue, or a blue first and then  white.<BR>\n" );
document.write( "P(white, blue) = (5/17)(4/17) = 20/289<BR>\n" );
document.write( "P(blue, white) = (4/17)(5,17) = 20/289<BR>\n" );
document.write( "P(one blue and one white) = 40/289<br><BR>\n" );
document.write( "(b)(ii) The probability of drawing a blue and then a red is (4/17)(8/17) = 32/289.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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