document.write( "Question 1206347: Question 17:
\n" ); document.write( "Thirty-five rose bushes are available from a nursery containing 16 red bushes, 11 yellow bushes, and 8 white bushes. 10 rose bushes are randomly chosen for replacement. What is the probability that no more than 8 red bushes are selected?
\n" ); document.write( " 0.9949
\n" ); document.write( " 0.9696
\n" ); document.write( " 0.9996
\n" ); document.write( " 0.0801\r
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Algebra.Com's Answer #843730 by ikleyn(52834) $\"\"$ $\"About$

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\n" ); document.write( "Thirty-five rose bushes are available from a nursery containing 16 red bushes,
\n" ); document.write( "11 yellow bushes, and 8 white bushes. 10 rose bushes are randomly chosen
\n" ); document.write( " $\"highlight%28cross%28for%29%29\"$ with replacement. What is the probability that no more than 8 red bushes are selected?
\n" ); document.write( "0.9949
\n" ); document.write( "0.9696
\n" ); document.write( "0.9996
\n" ); document.write( "0.0801
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document.write( "This experiment is with replacement, which means that the initial conditions\r\n" );
document.write( "are the same when selecting each next rose.\r\n" );
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document.write( "It implies that we have a binomial distribution probability, where the output\r\n" );
document.write( "at each trial/step is independent of other trials/steps.\r\n" );
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document.write( "So, use the standard binomial distribution function for cumulative probability\r\n" );
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document.write( "    P = P(n, k <= 8, p).\r\n" );
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document.write( "Here n is the total number of trials n=10; p =  =  = 0.457142857\r\n" );
document.write( "is the probability of selecting one of 16 particular items from the set of 35 items.\r\n" );
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document.write( "Use any of available methods of calculating this probability (regular calculator standard function\r\n" );
document.write( "binomcdf, or the Excel standard function BINOM.DIST in cumulative mode, or an online\r\n" );
document.write( "free of charge calculator https://stattrek.com/online-calculator/binomial.aspx\r\n" );
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document.write( "The answer is  P = 0.9949  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The key moment in the solution is to get that it is a binomial experiment.
\n" ); document.write( "The rest is just a mechanical exercise.\r
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