document.write( "Question 425873: Hello,
\n" ); document.write( "I have tried to solve a probability problem and have not reach any good answer. I would like someone to help me with this problem. Thank you!\r
\n" ); document.write( "\n" ); document.write( "Problem:
\n" ); document.write( "The numbers 1 through 9 are put into a hat. What is the probability that all odd numbers will be chosen first if one card at a time is drawn from the hat and not replaced? \n" ); document.write( "

Algebra.Com's Answer #296396 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
you have the number 1 through 9.
\n" ); document.write( "5 of those numbers are odd (1,3,5,7,9)
\n" ); document.write( "4 of those numbers are even (2,4,6,8)\r
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\n" ); document.write( "\n" ); document.write( "if he wants to draw all odd cards from the deck, then it will require a minimum of 5 draws from the deck.\r
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\n" ); document.write( "\n" ); document.write( "the probability that the first card is odd is equal to 5/9
\n" ); document.write( "the probability that the second card is odd is equal to 4/8
\n" ); document.write( "the probability that the third card is odd is equal to 3/7
\n" ); document.write( "the probability that the fourth card is odd is equal to 2/6
\n" ); document.write( "the probability that the fifth card is odd is equal to 1/5\r
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\n" ); document.write( "\n" ); document.write( "the probability that all 5 odd cards will be drawn from the deck in 5 draws from the deck is:\r
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\n" ); document.write( "\n" ); document.write( "5/9 * 4/8 * 3/7 * 2/6 * 1/5\r
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\n" ); document.write( "\n" ); document.write( "the total probability becomes .007936508\r
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\n" ); document.write( "\n" ); document.write( "to see how this works, use smaller numbers.\r
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\n" ); document.write( "\n" ); document.write( "suppose you have 3 numbers (1,2,3)\r
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\n" ); document.write( "\n" ); document.write( "p(getting all odd) would require a minimum of 2 draws.\r
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\n" ); document.write( "\n" ); document.write( "p(odd on first draw) = 2/3
\n" ); document.write( "p(odd on second draw) = 1/2\r
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\n" ); document.write( "\n" ); document.write( "p(odd on first and second draw) = 2/6\r
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\n" ); document.write( "\n" ); document.write( "here are the possible combination when you draw 2 cards out of 3.\r
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\r\n" );
document.write( "first draw      second draw     combination\r\n" );
document.write( "     1              2           1 odd 1 even\r\n" );
document.write( "     2              1           1 even 1 odd\r\n" );
document.write( "     1              3           2 odd *****\r\n" );
document.write( "     3              1           2 odd *****\r\n" );
document.write( "     2              3           1 even 1 odd\r\n" );
document.write( "     3              2           1 odd 1 even\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "only 2 out of 6 possible combinations have all odd numbers.
\n" ); document.write( "same idea works with your problem.
\n" ); document.write( "answer for your problem is:\r
\n" ); document.write( "\n" ); document.write( "(5*4*3*2*1) / (9*8*7*6*5) = .007936508\r
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