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).

A. 125 B. 1024 C. 1554 C. 2048 D. 15447

Solution.

Note that if X = n, then the last four rolls are 6’s, the one just before was not a 6, and there

were no four consecutive 6’s on the n - 5 rolls before that.

The solution is the p(x)=n= (1/6)^4 * 5/6* P (x> n -5)

I do not understand the P x > n-5 part in this equation. Can someone explain this with an example by choosing a value for n.

the last roll) a fair six-sided dice until you get 4 consecutive 6's. Find E(X).

A. 125 B. 1024 C. 1554 C. 2048 D. 15447

Solution.

Note that if X = n, then the last four rolls are 6’s, the one just before was not a 6, and there

were no four consecutive 6’s on the n - 5 rolls before that.

The solution is the p(x)=n= (1/6)^4 * 5/6* P (x> n -5)

I do not understand the P x > n-5 part in this equation. Can someone explain this with an example by choosing a value for n.

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