document.write( "Question 1206643: Six different colored dice are rolled. Of interest is the number of dice that show a \"1.\"
\n" ); document.write( "In words, define the Random Variable X.
\n" ); document.write( "the outcome of the roll of the dice
\n" ); document.write( "the color of the dice
\n" ); document.write( "how many dice are rolled
\n" ); document.write( "how many dice show a \"1\"
\n" ); document.write( "List the values that X may take on.
\n" ); document.write( "X = two, four, six
\n" ); document.write( "X = zero, one, two, three, four, five, six
\n" ); document.write( "X = 1
\n" ); document.write( "X = one, two, three, four, five, six
\n" ); document.write( "Give the distribution of X. (Enter the probability as a fraction.)
\n" ); document.write( "On average, how many dice would you expect to show a \"1\"?
\n" ); document.write( "Find the probability that all six dice show a \"1.\" (Round your answer to five decimal places.) \n" ); document.write( "

Algebra.Com's Answer #844267 by ikleyn(52787) $\"\"$ $\"About$

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Six different colored dice are rolled. Of interest is the number of dice that show a \"1.\"
\n" ); document.write( "(a) In words, define the Random Variable X.
\n" ); document.write( "the outcome of the roll of the dice
\n" ); document.write( "the color of the dice
\n" ); document.write( "how many dice are rolled
\n" ); document.write( "how many dice show a \"1\"
\n" ); document.write( "(b) List the values that X may take on.
\n" ); document.write( "X = two, four, six
\n" ); document.write( "X = zero, one, two, three, four, five, six
\n" ); document.write( "X = 1
\n" ); document.write( "X = one, two, three, four, five, six
\n" ); document.write( "(c) Give the distribution of X. (Enter the probability as a fraction.)
\n" ); document.write( "(d) On average, how many dice would you expect to show a \"1\"?
\n" ); document.write( "(e) Find the probability that all six dice show a \"1.\" (Round your answer to five decimal places.)
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document.write( "(a)  \r\n" );
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document.write( "     the outcome of the roll of the dice\r\n" );
document.write( "     the color of the dice\r\n" );
document.write( "     how many dice are rolled              <<<---=== to answer correctly, it is enough to read the post.\r\n" );
document.write( "     how many dice show a \"1\"\r\n" );
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document.write( "(b)  \r\n" );
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document.write( "     X = two, four, six\r\n" );
document.write( "     X = zero, one, two, three, four, five, six   <<<---===  to answer correctly, it is enough to think 7 seconds\r\n" );
document.write( "     X = 1\r\n" );
document.write( "     X = one, two, three, four, five, six\r\n" );
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document.write( "(c)  To calculate the probabilities P(0), P(1), P(2), . . . , P(6), use the formulas of a binomial distribution\r\n" );
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document.write( "     P(0) = ,\r\n" );
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document.write( "     P(1) =  = ,\r\n" );
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document.write( "     P(2) =  = ,\r\n" );
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document.write( "     . . . and so on . . . \r\n" );
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document.write( "     P(5) =  = ,\r\n" );
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document.write( "     P(6) = .\r\n" );
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document.write( "(d)  mean = 0*P(0) + 1*P(1) + 2*P(2) + . . . + 5*(P5) + 6*P(6) = \r\n" );
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document.write( "      = 1.\r\n" );
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document.write( "     The mean is 1.00.\r\n" );
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document.write( "(e)  P(6) =  = 0.0000214335,  or 0.00002 rounded to 5 decimals.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in full.\r
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