document.write( "Question 1041019: What is the probability that 6 rolls of a fair die will show four exactly 5 times? \n" ); document.write( "
Algebra.Com's Answer #655937 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You can see this is very very unlikely.\r\n" );
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document.write( "If an event is repeated n times with a probability of success \r\n" );
document.write( "each time is p, then the probability of getting exactly x \r\n" );
document.write( "successes is given by the binomial formula:\r\n" );
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document.write( "\"%28nCx%29p%5Ex%2A%281-p%29%5E%28n-x%29\"\r\n" );
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document.write( "You case is n=6 trials (rolls)\r\n" );
document.write( "The probability of a success (four) each time is p=1/6  \r\n" );
document.write( "The number of successes x=5\r\n" );
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document.write( "\"%286C5%29%281%2F6%29%5E5%2A%281-1%2F6%29%5E%286-5%29\"\r\n" );
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document.write( "\"%286%29%281%2F6%5E5%29%2A%285%2F6%29%5E%281%29\"\r\n" );
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document.write( "\"%286%29%281%2F7776%29%2A%285%2F6%29\"\r\n" );
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document.write( "\"%28cross%286%29%29%281%2F7776%29%2A%285%2Fcross%286%29%29\"\r\n" );
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document.write( "\"5%2F7776\"\r\n" );
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document.write( "Edwin
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