The events A and B are the outcomes of the probabilities in the system
The entropy of the system is 0
The probabilities are given as:
P(A) = 10/10
P(B) = 0/10
The entropy is calculated using:
[tex]H(x) = -\sum \limits^{n}_{i = 1} p_i * \log_2(p_i)[/tex]
So, we have
[tex]H(x) = -10/10 * \log_2(10/10) - 0/10 * \log_2(0/10)[/tex]
Evaluate the products
[tex]H(x) = -\log_2(10/10) - 0[/tex]
Evaluate the sum
[tex]H(x) = -\log_2(10/10)[/tex]
Evaluate the quotient
[tex]H(x) =- \log_2(1)[/tex]
Express 1 as 2^0
[tex]H(x) =- \log_2(2^0)[/tex]
Apply the power rule of logarithm
[tex]H(x) =- 0\log_2(2)[/tex]
Evaluate the product
H(x) =0
Hence, the entropy of the system is 0
Read more about probability at:
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