At noon on any given day, the probabilities that Kersley is asleep and that Kersley is studying are $0.2$ and $0.6$ respectively.
(i)[3]
Determine the probability that, over any $7$-day interval, Kersley is either asleep or studying at noon on at least $6$ days.
(ii)[5]
Use an approximation to determine the probability that, in a period of $100$ days, Kersley is asleep at noon on no more than $30$ days.
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