document.write( "Question 1192391: An unbiased dice with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum value is not less than 2 and maximum value is not greater than 5 is \n" ); document.write( "

Algebra.Com's Answer #824279 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "An unbiased dice with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times.
\n" ); document.write( "Out of four face values obtained, the probability that the minimum value
\n" ); document.write( "is not less than 2 and maximum value is not greater than 5 is
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\n" ); document.write( "\n" ); document.write( " \"dice\" is plural; a \"single\" form is \"die\".\r
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\n" ); document.write( "\n" ); document.write( " \"unbiased dice\" in this post means \"fair die\".\r
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document.write( "In the problem's formulation, \r\n" );
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document.write( "    \" the minimum value is not less than 2 and maximum value is not greater than 5\"\r\n" );
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document.write( "means that all upper-face values are between 2 and 5,  i.e. are from the interval [2,3,4,5].\r\n" );
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document.write( "For each individual rolling, the probability to have the upper-face value in this interval is  = .\r\n" );
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document.write( "So, we have the binomial distribution experiment with the number of trials 4; the probability of successful trial of 2/3\r\n" );
document.write( "and the complement probability of unsuccessful trial of  1/3.\r\n" );
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document.write( "Hence, the probability under the problem's question  is\r\n" );
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document.write( "    P =  =  = 0.197531   (rounded).    ANSWER\r\n" );
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