document.write( "Question 1157266: On the leeward side of the island of Oahu, in a small village, about 76% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
\n" ); document.write( "(a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.)
\n" ); document.write( "P(n) = ?\r
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Algebra.Com's Answer #780099 by Edwin McCravy(20066)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Theoretically you may never encounter a person of Hawaiian ancestry, but that is\r\n" );
document.write( "very unlikely, but we treat this as an infinite tree diagram.\r\n" );
document.write( "\"Yes\" means the person we meet is of Hawaiian ancestry, and \"no\" means they\r\n" );
document.write( "aren't.\r\n" );
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document.write( "      0.24   0.24   0.24   0.24   0.24   0.24   0.24 ... = (0.24)n+\r\n" );
document.write( "start—————no—————no—————no—————no—————no—————no————— ...\r\n" );
document.write( "     \      \      \      \      \      \      \     ...\r\n" );
document.write( "      \0.76  \0.76  \0.76  \0.76  \0.76  \0.76  \    ...\r\n" );
document.write( "       \      \      \      \      \      \      \   ... \r\n" );
document.write( "        yes    yes    yes    yes    yes    yes       ... \r\n" );
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document.write( "The probability that we will meet such a person the 1st time is\r\n" );
document.write( "0.76\r\n" );
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document.write( "The probability that we will not meet such a person until the 2nd time \r\n" );
document.write( "we meet somebody is (0.24)(0.76)\r\n" );
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document.write( "The probability that we will not meet such a person until the 3rd time\r\n" );
document.write( "we meet somebody is (0.24)2(0.76)\r\n" );
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document.write( "The probability that we will not meet such a person until the 4th time\r\n" );
document.write( "we meet somebody is (0.24)3(0.76)\r\n" );
document.write( "...\r\n" );
document.write( "...\r\n" );
document.write( "...\r\n" );
document.write( "The probability that we will not meet such a person until the nth time\r\n" );
document.write( "we meet somebody is (0.24)n-1(0.76)\r\n" );
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document.write( " n   P(n)\r\n" );
document.write( "---  ----\r\n" );
document.write( " 1   0.76\r\n" );
document.write( " 2   0.24(0.76)  \r\n" );
document.write( " 3   0.242(0.76)\r\n" );
document.write( " 4   0.243(0.76)\r\n" );
document.write( " .\r\n" );
document.write( " .\r\n" );
document.write( " .\r\n" );
document.write( " n   0.24n-1(0.76)\r\n" );
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document.write( "P(n) = 0.24n-1(0.76)  \r\n" );
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document.write( "Edwin
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