document.write( "Question 1160576: A fair coin is tossed repeatedly until a head is obtained. The probability that the coin has to be tossed at least four times is...........................................?
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Algebra.Com's Answer #783893 by ikleyn(52906) $\"\"$ $\"About$

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document.write( "The problem asks to find the probability to have a head UNDER THE CONDITION that the three first tosses give a tail.\r\n" );
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document.write( "It is the sum of probabilities\r\n" );
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document.write( "    P = P(4) + P(5) + P(6) + . . . \r\n" );
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document.write( "where P(4) is the probability to get H first time at the 4-th toss;\r\n" );
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document.write( "      P(5) is the probability to get H first time at the 5-th toss, assuming that the outcome was T at the 4-th toss;\r\n" );
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document.write( "      P(6) is the probability to get H first time at the 6-th toss, assuming that the outcome was T at the 4-th and 5-th toss,\r\n" );
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document.write( "      and so on . . . (infinite sum)\r\n" );
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document.write( "Notice that  P(4) = P(TTTH) = ;  \r\n" );
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document.write( "             P(5) = .P(TTTTH) =  = ;\r\n" );
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document.write( "             P(6) = .P(TTTTTH) =  =  ,   and so on . . . \r\n" );
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document.write( "So,  P is the sum of the infinite geometric progression with the first term    and the common ratio of  = .\r\n" );
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document.write( "The sum of this progression is  P =  =  =  =  = 0.083333...   \r\n" );
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document.write( "It is the ANSWER to this problem.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Notice that my answer is different from the solution by Edwin, and the logic is DIFFERENT, too.\r
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