document.write( "Question 1101847: What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? (Use a 365-day year. Round your answer to four decimal places.) \n" ); document.write( "

Algebra.Com's Answer #716490 by ikleyn(52915) $\"\"$ $\"About$

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document.write( "The full space of events is the set of all records of the length 9; each the record contains 9 numbers: \r\n" );
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document.write( "one number from 1 to 365 (the birthday) in each position from 1 to 9. \r\n" );
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document.write( "The full set contains    records/elements.\r\n" );
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document.write( "The complement set consists of those records that have no two equal numbers in all 9 positions (no repetition allowed)\r\n" );
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document.write( "    1)  we can select any of               365 numbers in the 1-st position,\r\n" );
document.write( "    2)  we can select any of the remaining 364 numbers in the 2-nd position,\r\n" );
document.write( "    . . . \r\n" );
document.write( "    and so on . . . till\r\n" );
document.write( "    . . . \r\n" );
document.write( "    8)  we can select any of the remaining 358 numbers in the 8-th position,\r\n" );
document.write( "    9)  we can select any of the remaining 357 numbers in the 9-th position.\r\n" );
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document.write( "In all, the complementary set has  365*364*363*362*361*360*359*358*357  records/elements.\r\n" );
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document.write( "Therefore, the probability under the question is      -  = 0.0946.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Also, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Elementary Probability problems related to combinations, Problem 7\r
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