Question: A certain television show airs weekly. Each time it airs, its ratings are categorized as high, average, or low, and transitions between these categorization each

A certain television show airs weekly. Each time it airs, its ratings are categorized as high, average, or low, and transitions between these categorization each week behave like a Markov chain. If the ratings are average this week, they will be high, average, or low next week with probabilities 60%, 40%, and 0% respectively. If ratings are average this week, they will be high, average, or low next week with probabilities 10%, 50%, and 40% respectively. If the ratings are low this week, they will be high, average, or low next week with probabilities 50%, 30%, and 20% respectively. Write all answers as integers or decimals.

If the ratings are average this week, what is the probability that they will be low two weeks from now?

If the ratings are average the first week, what is the probability that they will be low the second week?

If the ratings are low the first week, what is the probability that they will be high the third week?

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