document.write( "Question 1166511: We are rolling a 6 sided die. Let A be the random event of how many rolls it takes to roll your first 4. What is the probability mass function and prove that the values of f(x) add up to 1. \n" ); document.write( "

Algebra.Com's Answer #791059 by Edwin McCravy(20065) $\"\"$ $\"About$

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document.write( "The probability that the 1st roll is a 4 is \r\n" );
document.write( ", the 1st term\r\n" );
document.write( "The probability that the 1st roll is not a 4 and the 2nd one is a 4 is\r\n" );
document.write( ", the 2nd term\r\n" );
document.write( "The probability that the 1st 2 rolls are not 4's and the 3rd one is a 4 is\r\n" );
document.write( ", the 3rd term\r\n" );
document.write( "The probability that the 1st 3 rolls are not 4's and the 4th one is a 4 is\r\n" );
document.write( ", the 4th term\r\n" );
document.write( "...\r\n" );
document.write( "The probability that the 1st x-1 rolls are not 4's and the xth one is a 4 is\r\n" );
document.write( ", the xth term\r\n" );
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document.write( "So\r\n" );
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document.write( "Notice that theoretically (mathematically) it could take you a billion\r\n" );
document.write( "rolls, or a million years, [lol] to roll your first 4. [if you had an\r\n" );
document.write( "extremely stubborn die!!!]\r\n" );
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document.write( "The sum of all values of f(x) is an infinite series and the sum of the\r\n" );
document.write( "infinite series is:\r\n" );
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document.write( "where a₁ = first term = 1/6, and r = 5/6\r\n" );
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document.write( "Edwin

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