E(X): Find Probability of Rolling 4 Consecutive 6's with a Fair Dice

[undertoes]

Let X be a random variable representing the number of times you need to roll (including the last roll) a fair six-sided dice until you get 4 consecutive 6's. Find E(X)?
answer is 1554.

I get confused with this, probability { X > n-5 }. I know that the last for throws must be 6's and the one before 'n-4 throws' must not be a 6. Any input please?

 

[undertoes]

anyone?

 

[EnumaElish]

The probability that 4 of 4 throws are all sixes is q = 1/6^4. X is distributed Geometric with success probability q, and each "trial" represents four consecutive throws.

An alternative approach may be to calculate Prob{a 4-run of sixes} = 1 - Prob{not having a 4-run of sixes} using the binomial formula.