document.write( "Question 277919: Statistics - 5 items in drawer (A,B,C,D,E). Choose 2 with replacement.
\n" ); document.write( "P(same letter)
\n" ); document.write( "P(A and B)
\n" ); document.write( "P(A or B)
\n" ); document.write( "P(A and B/1st selection A)
\n" ); document.write( "P(A and B/1st selection not E)\r
\n" ); document.write( "\n" ); document.write( "I know there are 120 outcomes\r
\n" ); document.write( "\n" ); document.write( "Sample Space\r
\n" ); document.write( "\n" ); document.write( "ABCDE BACDE CABDE DABCE EABCD
\n" ); document.write( "ABCED BACED CABED DABEC EABDC
\n" ); document.write( "ABDCE BADCE CADBE DACBE EACBD
\n" ); document.write( "ABDEC BADEC CADEA DACEB EACDB
\n" ); document.write( "ABECD BAECD CAEBD DAEBC EADBC
\n" ); document.write( "ABEDC BAEDC CAEDB DAECB EADCB
\n" ); document.write( "ACBDE BCADE CBADE DBACE EBACD
\n" ); document.write( "ACBED BCAED CBAED DBAEC EBADC
\n" ); document.write( "ACDBE BCDAE CBDAE DBCAE EBCAD
\n" ); document.write( "ACDEB BCDEA CBDEA DBCEA EBCDA
\n" ); document.write( "ACEBD BCEAD CBEAD DBEAC EBDAC
\n" ); document.write( "ACEDB BCEDA CBEDA DBECA EBDCA
\n" ); document.write( "ADBCE BDACE CDABE DCABE ECABD
\n" ); document.write( "ADBEC BDAEC CDAEB DCAEB ECADB
\n" ); document.write( "ADCBE BDCAE CDBAE DCBAE ECBAD
\n" ); document.write( "ADCEB BDCEA CDBEA DCBEA ECBDA
\n" ); document.write( "ADEBC DCEAC CDEAB DCEAB ECDAB
\n" ); document.write( "ADECB BDECA CDEBA DCEBA ECDBA
\n" ); document.write( "AEBCD BEACD CEABD DEABC EDABC
\n" ); document.write( "AEBDC VEADC CEADB DEACB EDACB
\n" ); document.write( "AECBD BECAD CEBAD DEBAC EDBAC
\n" ); document.write( "AECDB BECDA CEBDA DEBCA EDBCA
\n" ); document.write( "AEDBC BEDAC CEDAB DECAB EDCAB
\n" ); document.write( "AEDCB DEDCA CEDBA DECBA EDCBC \n" ); document.write( "
Algebra.Com's Answer #202304 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
Statistics - 5 items in drawer (A,B,C,D,E). Choose 2 with replacement.\r
\n" ); document.write( "\n" ); document.write( "5 items in drawer (A,B,C,D,E). Choose 2 with replacement.
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\r\n" );
document.write( "You have listed the wrong sample space!  The sample space you \r\n" );
document.write( "listed is the 5! or 120 ways or rearranging all the items in a row.\r\n" );
document.write( "This is NOT what we are doing in this problem.  What we are doing \r\n" );
document.write( "is drawing one item, replacing it, and then drawing another.\r\n" );
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document.write( "Here is the sample space, where, for example (C,B) means that\r\n" );
document.write( "C was drawn first then B was drawn second. \r\n" );
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document.write( "(A,A)  (A,B)  (A,C)  (A,D)  (A,E)\r\n" );
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document.write( "(B,A)  (B,B)  (B,C)  (B,D)  (B,E)\r\n" );
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document.write( "(C,A)  (C,B)  (C,C)  (C,D)  (C,E)\r\n" );
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document.write( "(D,A)  (D,B)  (D,C)  (D,D)  (D,E)\r\n" );
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document.write( "(E,A)  (E,B)  (E,C)  (E,D)  (E,E)\r\n" );
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document.write( "--------------------\r\n" );
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\n" ); document.write( "P(same letter)
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\r\n" );
document.write( "(A,A)  (A,B)  (A,C)  (A,D)  (A,E)\r\n" );
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document.write( "(B,A)  (B,B)  (B,C)  (B,D)  (B,E)\r\n" );
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document.write( "(C,A)  (C,B)  (C,C)  (C,D)  (C,E)\r\n" );
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document.write( "(D,A)  (D,B)  (D,C)  (D,D)  (D,E)\r\n" );
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document.write( "(E,A)  (E,B)  (E,C)  (E,D)  (E,E)\r\n" );
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document.write( "I've colored the ones with the same letter red.\r\n" );
document.write( "So there are 5 out of 25 and the probability is \"5%2F25=1%2F5\"\r\n" );
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document.write( "--------------------\r\n" );
document.write( "

\n" ); document.write( "P(A and B)
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\r\n" );
document.write( "(A,A)  (A,B)  (A,C)  (A,D)  (A,E)\r\n" );
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document.write( "(B,A)  (B,B)  (B,C)  (B,D)  (B,E)\r\n" );
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document.write( "(C,A)  (C,B)  (C,C)  (C,D)  (C,E)\r\n" );
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document.write( "(D,A)  (D,B)  (D,C)  (D,D)  (D,E)\r\n" );
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document.write( "(E,A)  (E,B)  (E,C)  (E,D)  (E,E)\r\n" );
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document.write( "I've colored the ones with both an A and a B red.\r\n" );
document.write( "So there are 2 out of 25 and the probability is \"2%2F25\" \r\n" );
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document.write( "--------------------\r\n" );
document.write( "

\n" ); document.write( "P(A or B)
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\r\n" );
document.write( "(A,A)  (A,B)  (A,C)  (A,D)  (A,E)\r\n" );
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document.write( "(B,A)  (B,B)  (B,C)  (B,D)  (B,E)\r\n" );
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document.write( "(C,A)  (C,B)  (C,C)  (C,D)  (C,E)\r\n" );
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document.write( "(D,A)  (D,B)  (D,C)  (D,D)  (D,E)\r\n" );
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document.write( "(E,A)  (E,B)  (E,C)  (E,D)  (E,E)\r\n" );
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document.write( "I've colored the ones with either an A or a B red.\r\n" );
document.write( "So there are 16 out of 25 and the probability is \"16%2F25\"\r\n" );
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document.write( "---------------------\r\n" );
document.write( "

\n" ); document.write( "P(A and B|1st selection A)
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\r\n" );
document.write( "(A,A)  (A,B)  (A,C)  (A,D)  (A,E)\r\n" );
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document.write( "(B,A)  (B,B)  (B,C)  (B,D)  (B,E)\r\n" );
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document.write( "(C,A)  (C,B)  (C,C)  (C,D)  (C,E)\r\n" );
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document.write( "(D,A)  (D,B)  (D,C)  (D,D)  (D,E)\r\n" );
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document.write( "(E,A)  (E,B)  (E,C)  (E,D)  (E,E)\r\n" );
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document.write( "Notice that since we are given that the 1st selection\r\n" );
document.write( "was A, then we eliminate all the members of the sample\r\n" );
document.write( "space except those that have the given condition, namely\r\n" );
document.write( "that the first selection was A.  Above I have lined through\r\n" );
document.write( "all the ones that are eliminated by the given condition\r\n" );
document.write( "that the first selection is A. That leaves only 5 \r\n" );
document.write( "members of the reduced sample space, and (A,B) is the \r\n" );
document.write( "only successful one, so the probability is \"1%2F5\"\r\n" );
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document.write( "--------------------\r\n" );
document.write( "

\n" ); document.write( "P(A and B/1st selection not E)
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\r\n" );
document.write( "(A,A)  (A,B)  (A,C)  (A,D)  (A,E)\r\n" );
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document.write( "(B,A)  (B,B)  (B,C)  (B,D)  (B,E)\r\n" );
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document.write( "(C,A)  (C,B)  (C,C)  (C,D)  (C,E)\r\n" );
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document.write( "(D,A)  (D,B)  (D,C)  (D,D)  (D,E)\r\n" );
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document.write( "(E,A)  (E,B)  (E,C)  (E,D)  (E,E)\r\n" );
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document.write( "Notice that since we are given that the 1st selection\r\n" );
document.write( "was not E, then we eliminate all the members of the sample\r\n" );
document.write( "space except those that have the given condition, namely\r\n" );
document.write( "that the first selection was not E.  Above I have lined through\r\n" );
document.write( "all the ones that are eliminated by the given condition\r\n" );
document.write( "that the first selection is not E.  That leaves only 20 \r\n" );
document.write( "members of the reduced sample space, and (A,B) and (B,A) are\r\n" );
document.write( "the only successful ones, so the probability is \"2%2F20=1%2F10\"\r\n" );
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document.write( "Edwin
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