document.write( "Question 1171755: Sam is at the origin in the coordinate plane. Every minute, he flips a coin. If he gets
\n" ); document.write( "heads, he walks right one unit. Otherwise, he walks left one unit. After five minutes,
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Algebra.Com's Answer #796682 by ikleyn(52908) $\"\"$ $\"About$

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document.write( "The meaning / (the context) of this problem is that Sam flips the coin at the beginning of each minute t= 0, 1, 2, 3, 4,\r\n" );
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document.write( "and, depending on the result of each individual flipping, he is 1 unit to the left or 1 unit to the right \r\n" );
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document.write( "from his previous/(current) position on the straight line at the end of THIS minute.\r\n" );
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document.write( "Let H be the number of Heads in 5 flips.\r\n" );
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document.write( "Then the number of Tails is (5-H), and we are interested to find the value of H under this condition\r\n" );
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document.write( "    H - (5-H) = 1.\r\n" );
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document.write( "From the equation,\r\n" );
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document.write( "    H - 5 + H = 1,   2H = 1 + 5 = 6,   H = 6/2 = 3.\r\n" );
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document.write( "Thus, to get the point 1 unit to the right from the beginning after 5 flips, he should have 3 Heads and 2 Tails in his experiment.\r\n" );
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document.write( "What concretely is the sequence of heads and tails in the experiment, it DOES NOT matter.\r\n" );
document.write( "What does really matter, is to have  3  Heads and  2  Tails in any order of  5 flips.\r\n" );
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document.write( "So, it is a binomial distribution problem with the number of trials n= 5 and the number of success k= 3; \r\n" );
document.write( "the probability of the success is  = 0.5 in each individual trial.\r\n" );
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document.write( "THEREFORE, the probability under the problem's question is  P =  =  = 0.3125.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a good entertainment problem.\r
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\n" ); document.write( "\n" ); document.write( "By the way, with 6 flips the probability to get the point (1,0) is equal to ZERO,
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