document.write( "Question 737203: a coin is tossed until for the first time the same result occurs in twice succession.Find the probability that an even number of tosses is required. \n" ); document.write( "

Algebra.Com's Answer #450256 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "To be successful you either have to get\r\n" );
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document.write( "HH or HTHH or HTHTHH or HTHTHTHH\r\n" );
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document.write( "or get\r\n" );
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document.write( "TT or THTT or THTHTT or THTHTHTT\r\n" );
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document.write( "So it's the probability of starting with a head and\r\n" );
document.write( "ending with two heads + the probability of starting \r\n" );
document.write( "with a tail and ending with two tails.\r\n" );
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document.write( "The desired probability is the sum of sums of these \r\n" );
document.write( "two infinite geometric series:\r\n" );
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document.write( "1.   P(HH)+P(HTHH)+P(HTHTHH)+ЗЗЗ =  \r\n" );
document.write( "+ЗЗЗ =\r\n" );
document.write( "+ЗЗЗ   \r\n" );
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document.write( "2.   P(TT)+P(THTT)+P(THTHTT)+ЗЗЗ =  \r\n" );
document.write( " +ЗЗЗ =\r\n" );
document.write( "+ЗЗЗ   \r\n" );
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document.write( "Each of those has a₁= and r =\r\n" );
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document.write( "S_∞ =  =  =  =  = \r\n" );
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document.write( "So the desired probability is twice that or \r\n" );
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document.write( "Edwin

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