document.write( "Question 293293: A fair coin is tossed until first tail comes up. Let A be the event that the number of tosses is divisible by 5, b be the event that the number of tosses is less than 6\r
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Algebra.Com's Answer #211748 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
A fair coin is tossed until first tail comes up. Let A be the event that the number of tosses is divisible by 5, \r
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document.write( "The other tutor's solution is incorrect.\r\n" );
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document.write( "P(A) = P(x=5 or x=10 or x=15 or ... x=5n or ...)\r\n" );
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document.write( "Since \"or\" implies \"add\"\r\n" );
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document.write( "P(A) = P(x=5) + P(x=10) + P(x=15) + ... + P(x=5n) + ...\r\n" );
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document.write( "P(x=5) = \"%281%2F2%29%5E5\", which means the 5 tosses went HHHHT \r\n" );
document.write( "P(x=10) = \"%281%2F2%29%5E10\" which means the 10 tosses went HHHHHHHHHT\r\n" );
document.write( "P(x=15) = \"%281%2F2%29%5E15\" which means the 15 tosses went HHHHHHHHHHHHHHT\r\n" );
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document.write( "P(x=5n) = \"%281%2F2%29%5E%285n%29\"\r\n" );
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document.write( "P(A) = the sum of an infinite geometric series with \"a%5B1%5D=1%2F%282%5E5%29=1%2F32\"\r\n" );
document.write( "and \"r=%281%2F2%29%5E5=1%2F32\"\r\n" );
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document.write( "\"S%5Binfinity%5D=a%5B1%5D%2F%281-r%29=%281%2F32%29%2F%281-1%2F32%29=1%2F%2832-1%29=1%2F31\"\r\n" );
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document.write( "P(B) = P(T or HT or HHT or HHHT or HHHHT or HHHHT) =\r\n" );
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document.write( "Since \"or\" implies \"add\"\r\n" );
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document.write( "P(B) = P(T) + P(HT) + P(HHT) + P(HHHT) + P(HHHHT) =\r\n" );
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document.write( "P(B) = \"%281%2F2%29+%2B+%281%2F2%29%5E2+%2B+%281%2F2%29%5E3+%2B+%281%2F2%29%5E4+%2B+%281%2F2%29%5E5\" \r\n" );
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document.write( "P(B) = \r\n" );
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document.write( "Use the formula:\r\n" );
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document.write( "P(A U B) = P(A or B) = P(A) + P(B) - P(A and B)\r\n" );
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document.write( "We have P(A) = \"1%2F31\",  P(B) = \"31%2F32\"\r\n" );
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document.write( "The event \"A and B\" is the event HHHHT, the only event\r\n" );
document.write( "which would be both a multiple of 5 tosses and also less\r\n" );
document.write( "than 6 tosses.\r\n" );
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document.write( "HHHHT has probability \"%281%2F2%29%5E5=1%2F32\"=P(A and B)\r\n" );
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document.write( "P(A U B) = P(A or B) = P(A) + P(B) - P(A and B)\r\n" );
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document.write( "P(A U B) = P(A or B) = \"1%2F32+%2B+31%2F32+-+1%2F32=31%2F32\"\r\n" );
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document.write( "Edwin
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