Question: Codewords from the alphabet { 0 , 1 , 2 , 3 } are called legitimate if they have an even number of 0 '

Codewords from the alphabet {0,1,2,3} are called legitimate if they have an even
number of 0's. What's the probability of a codeword of length k is legitimate?
Hint: First show the recursion ak=2ak-1+4k-1, where ak is the number of legitimate
codewords of length k .
Codewords from the alphabet { 0 , 1 , 2 , 3 } are

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