document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205258>Question 1205258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 8 red marbles, 9 white marbles, and 6 blue marbles. You draw 5 marbles out at random, without replacement. For the following questions, round the answer to 3 decimals as required. What is the probability that all the marbles are red?\r<BR>\n" );
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document.write( "The probability that all the marbles are red is <BR>\n" );
document.write( "0.002<BR>\n" );
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document.write( "What is the probability that exactly two of the marbles are red?<BR>\n" );
document.write( "The probability that exactly two of the marbles are red is <BR>\n" );
document.write( "0.379<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "What is the probability that none of the marbles are red?<BR>\n" );
document.write( "The probability of picking no red marbles is <BR>\n" );
document.write( "0.089<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "are my answers correct? they're rounded to 3DP. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841930 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part 1<BR>\n" );
document.write( "8 red + 9 white + 6 blue = 23 marbles total<BR>\n" );
document.write( "A = P(1st is red) = 8/23<BR>\n" );
document.write( "B = P(2nd is red given 1st is red) = 7/22<BR>\n" );
document.write( "C = P(3rd is red given 1st 2 are red) = 6/21<BR>\n" );
document.write( "D = P(4th is red given 1st 3 are red) = 5/20<BR>\n" );
document.write( "E = P(5th is red given 1st 4 are red) = 4/19<BR>\n" );
document.write( "Note the countdown of numerators and denominators. <BR>\n" );
document.write( "I wouldn't reduce any of the fractions (or else you'll lose this countdown).<BR>\n" );
document.write( "P(all 5 red) = A*B*C*D*E<BR>\n" );
document.write( "P(all 5 red) = (8/23)*(7/22)*(6/21)*(5/20)*(4/19)<BR>\n" );
document.write( "P(all 5 red) = 0.00166 approximately<BR>\n" );
document.write( "P(all 5 red) = <font color=red>0.002</font> when rounding to 3 decimal places<BR>\n" );
document.write( "<font color=red>You are correct.</font>\r<BR>\n" );
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document.write( "Part 2<BR>\n" );
document.write( "8 red, 23 total, 23-8 = 15 marbles that aren't red<BR>\n" );
document.write( "A = P(1st is red) = 8/23<BR>\n" );
document.write( "B = P(2nd is red given 1st is red) = 7/22<BR>\n" );
document.write( "C = P(3rd is not red given events A and B) = 15/21<BR>\n" );
document.write( "D = P(4th is not red given previous events) = 14/20<BR>\n" );
document.write( "E = P(5th is not red given previous events) = 13/19<BR>\n" );
document.write( "P(1st two marbles are red) = A*B*C*D*E <BR>\n" );
document.write( "P(1st two marbles are red) = (8/23)*(7/22)*(15/21)*(14/20)*(13/19)<BR>\n" );
document.write( "P(1st two marbles are red) = 0.03786 approximately<BR>\n" );
document.write( "That's just for the first two marbles being red. <BR>\n" );
document.write( "But we have 5C2 = 10 combinations of arranging these red marbles. <BR>\n" );
document.write( "Refer to the nCr combination formula.<BR>\n" );
document.write( "We multiply that previous result by 10 to get 10*0.03786 = 0.3786 and that rounds to <font color=red>0.379</font><BR>\n" );
document.write( "<font color=red>You are correct.</font><BR>\n" );
document.write( "This has a binomial-like feel to it, but it's not entirely the binomial probability formula (note how the trials are <u>not</u> independent).\r<BR>\n" );
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document.write( "Part 3<BR>\n" );
document.write( "8 red, 23 total, 23-8 = 15 not red<BR>\n" );
document.write( "A = P(1st is not red) = 15/23<BR>\n" );
document.write( "B = P(2nd is not red given event A happened) = 14/22<BR>\n" );
document.write( "C = P(3rd is not red given events A,B happened) = 13/21<BR>\n" );
document.write( "D = P(4th is not red given events A,B,C happened) = 12/20<BR>\n" );
document.write( "E = P(5th is not red given events A,B,C,D happened) = 11/19<BR>\n" );
document.write( "P(no red) = A*B*C*D*E<BR>\n" );
document.write( "P(no red) = (15/23)*(14/22)*(13/21)*(12/20)*(11/19)<BR>\n" );
document.write( "P(no red) = 0.08924 approximately<BR>\n" );
document.write( "P(no red) = <font color=red>0.089</font><BR>\n" );
document.write( "<font color=red>You are correct.</font>\r<BR>\n" );
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document.write( "Nice work on getting all three parts correct. <BR>\n" );
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