Negative binomial distribution

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Homework Statement

Repeatdly roll a fair die until the outcome 3 has accurred on the 4th roll. Let
X be the number of times needed in order to achieve this goal. Find E(X)
and Var(X)

Homework Equations

The Attempt at a Solution

I am having trouble deciphering this question. Is the first sentence saying to roll a die until you get a 3 on the fourth roll? thus the event of a success is when you get a 3 on the fourth roll? but what is number of successes? which you need to know in order to find the mean in a negative binomial distribution.

Apparently E(X) = 24.

 

[Ray Vickson]

Homework Statement

Repeatdly roll a fair die until the outcome 3 has accurred on the 4th roll. Let
X be the number of times needed in order to achieve this goal. Find E(X)
and Var(X)

Homework Equations

The Attempt at a Solution

I am having trouble deciphering this question. Is the first sentence saying to roll a die until you get a 3 on the fourth roll? thus the event of a success is when you get a 3 on the fourth roll? but what is number of successes? which you need to know in order to find the mean in a negative binomial distribution.

Apparently E(X) = 24.

Please clarify: do you mean the first 1, 2 or 3 tosses could also result in a "3", and that you look only at the result of the fourth toss? Or, do you mean that you count the rolls only if the first three are non-3s and the fourth is a 3? It makes a huge difference!