document.write( "Question 309610: Four jelly beans are selected, one at a time from a bowl containing 6 black, 6 red and 6 green jelly beans. Let x represent the number of black jelly beans selected in 4 draws from the bowl.
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\n" ); document.write( "(A) If this experiment is completed without replacing the jelly beans, explain why x is not a binomial random variable.
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\n" ); document.write( "(B) If this experiment is completed with replacement of the jelly beans, explain why x is a binomial random variable.
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Algebra.Com's Answer #221433 by Edwin McCravy(20056) $\"\"$ $\"About$

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Four jelly beans are selected, one at a time from a bowl containing 6 black, 6 red and 6 green jelly beans. Let x represent the number of black jelly beans selected in 4 draws from the bowl. \r
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\n" ); document.write( "(B) If this experiment is completed with replacement of the jelly beans, explain why x is a binomial random variable.
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document.write( "If x is a binomial random variable, then p, the probability of selecting 1\r\n" );
document.write( "black jelly bean in 1 trial, must not be different in any of the 4 selections\r\n" );
document.write( "of one jelly bean.  If you replace the jelly bean, as in (B), this probability\r\n" );
document.write( "p will not change, and x will be a binomial random variable.  However if you do\r\n" );
document.write( "not replace the jelly bean each time, as in (A), the probability will change each\r\n" );
document.write( "time you draw a jelly bean, and thus (A) will not allow x to be a binomial\r\n" );
document.write( "variable.\r\n" );
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document.write( "Another way of stating it is that if you do not replace the jelly bean each\r\n" );
document.write( "time, each successive trial (selection) will be DEPENDENT on what you drew\r\n" );
document.write( "before.  However if x is to be a binomial random variable, each selection\r\n" );
document.write( "(trial) must be INDEPENDENT of any other selection (trial).\r\n" );
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document.write( "Edwin

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