SOLUTION: 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
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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? Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! 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.
Let x=p and y=1-p
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.
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.
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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Ed
