Question: 11. Show that if un is the probability that n tosses of a fair coin contain no run of 4 heads, then for n

11. Show that if un is the probability that n tosses of a fair coin contain no run of 4 heads, then for n ≥ 4 un = 1 2un−1 + 1 4 un−2 + 1 8 un−3 + 1 16un−4.

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