Question

A child types the letters q, w, e, r, t, y, randomly producing 1000 letters in all. what is the expected number of times that the sequence qqqq appears, counting overlaps

Answer 1

1/6*1/6*1/6*1/6 = 1/1296 = 0.078% probability of ANY 4-letter sequence (including qqqq)
1000/1296 is less than 1.
Expected number of times qqqq (or any given 4-letter sequence) will appear in 1000 letters is 0.