document.write( "Question 1183213: A bag contains 10 red marbles, 8 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?\r
\n" ); document.write( "\n" ); document.write( "The probability that all the marbles are red is\r
\n" ); document.write( "\n" ); document.write( "This question I can solve, P(5xred) = (10/36)*(9/35)*(8/34)*(7/33)*(6/32) = 1/1496\r
\n" ); document.write( "\n" ); document.write( "What is the probability that exactly two of the marbles are red?
\n" ); document.write( "The probability that exactly two of the marbles are red is \r
\n" ); document.write( "\n" ); document.write( "I can't seem to get this one right. I assumed it just was (10/36)*(9/35) but that is not the case. I know that the \"exactly\" part is important I just don't know what to do in that case.\r
\n" ); document.write( "\n" ); document.write( "What is the probability that none of the marbles are red?
\n" ); document.write( "The probability of picking no red marbles is\r
\n" ); document.write( "\n" ); document.write( "This to be similar to the complement of the first question, but that does not give th right answer, I tried 1-((10/36)*(9/35)*(8/34)*(7/33)*(6/32)) which is incorrect. I have tried (16/36)*(15/35)*(14/34)*(13/33)*(12/32) but this is also incorrect. So I am stuck. I don't know what to do anymore. \n" ); document.write( "

Algebra.Com's Answer #813416 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A bag contains 10 red marbles, 8 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement.
\n" ); document.write( "(1) What is the probability that all the marbles are red?
\n" ); document.write( "The probability that all the marbles are red is
\n" ); document.write( "This question I can solve, P(5xred) = (10/36)*(9/35)*(8/34)*(7/33)*(6/32) = 1/1496\r
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\n" ); document.write( "\n" ); document.write( "(2) What is the probability that exactly two of the marbles are red?
\n" ); document.write( "The probability that exactly two of the marbles are red is
\n" ); document.write( "I can't seem to get this one right. I assumed it just was (10/36)*(9/35) but that is not the case.
\n" ); document.write( "I know that the \"exactly\" part is important I just don't know what to do in that case.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(3) What is the probability that none of the marbles are red?
\n" ); document.write( "The probability of picking no red marbles is
\n" ); document.write( "This to be similar to the complement of the first question, but that does not give th right answer,
\n" ); document.write( "I tried 1-((10/36)*(9/35)*(8/34)*(7/33)*(6/32)) which is incorrect. I have tried (16/36)*(15/35)*(14/34)*(13/33)*(12/32)
\n" ); document.write( "but this is also incorrect. So I am stuck. I don't know what to do anymore.
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document.write( "(1)  You INCORRECTLY calculated the answer to this question. \r\n" );
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document.write( "     The correct formula is  P = (10/26)*(9/25)*(8/24)*(7/23)*(6/22) = 0.003831    (approx.;  rounded).    ANSWER\r\n" );
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document.write( "(2)  In this case, the probability is THIS FRACTION\r\n" );
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document.write( "         P = .\r\n" );
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document.write( "     The denominator    is the number of all combinations of 26 marbles taken 5 at a time.\r\n" );
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document.write( "     In other words, it is the number of all possible 5-marble subsets of the given set of 26 marbles.\r\n" );
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document.write( "     It is so called \"the set of all possible events\" in this problem.\r\n" );
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document.write( "          =  = 65780.\r\n" );
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document.write( "     The numerator in the formula is the number of all possible 5-marble subsets, containing EXACTLY 2 red marbles.\r\n" );
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document.write( "     This number is   .  = 45 * 560 = 25200.\r\n" );
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document.write( "     THEREFORE, the final probability in this case is  P =  = 0.3831   (approx.; rounded).    ANSWER\r\n" );
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document.write( "(3)  In this case, you select from 16 non-red marbles;  so the probability is\r\n" );
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document.write( "         P = (16/26)*(15/25)*(14/24)*(13/23)*(12/22) = 0.0664    (approx.;  rounded).      ANSWER\r\n" );
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