The expected number of coin flips to get to 3 consecutive 1s or 4s in a row (meaning you can get 114, 111, 444, 411, etc) is 39. The expected number of coin flips to get 3 consecutive 1s in a row is 258.
A: The probability of getting 3 consecutive 1s/4s is (1/3)(1/3)(1/3) = 1/27
B: The probability of getting 3 consecutive 1s is (1/6)(1/6)(1/6) = 1/216 = 1/(27*8). TAKEAWAY: B IS 8X LESS LIKELY THAN A IS
Why is the expected number of coin flips to get B not 8 times the number of coin flips to get A? 8*39 = 312, not 258.