document.write( "Question 867202: Entertainment: an entertainment system has n speakers. Each speaker will function properly with probability p, independent of whether the other speakers are functioning. The system will operate effectively if at least 50% of it's speakers are functioning. For what values of p is a 4-speaker system more likely to operate than a 5-speaker system? \n" ); document.write( "

Algebra.Com's Answer #522924 by edjones(8007) $\"\"$ $\"About$

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Since each speaker is \"functioning properly\" or not we can expand a binomial and check which system is more likely to operate with different p values.
\n" ); document.write( "Let x=p and y=1-p
\n" ); document.write( "For 4 speakers: x^4+4x^3y+6x^2y^2 is the only part of the expansion (x+y)^4 in which at least 50% of the speakers are functioning.
\n" ); document.write( "For 5 speakers: x^5+5x^4y+10x^3y^2 is the only part of the expansion (x+y)^5 in which at least 50% of the speakers are functioning.
\n" ); document.write( "No matter what values of x are used the 4 speaker system is more likely to operate better than the 5.
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