32. Each of two switches is either on or off during a day. On day n, each...

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32. Each of two switches is either on or off during a day. On day n, each switch will independently be on with probability

[1 + number of on switches during day n āˆ’ 1]/4 For instance, if both switches are on during day nāˆ’1, then each will independently be on during day n with probability 3/4. What fraction of days are both switches on? What fraction are both off?

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