A fair 6-sided die is thrown repeatedly until two different numbers appear. What is the expected number of rolls?
My intuition tells that this is a geometric distribution with parameter $(\dfrac{5}{6})$ . So the expected value is $\dfrac{6}{5}$. But I am not sure. The place where I am confused is a general geometric distribution random variable is defined by its pdf $P(X=k) = (1-p)^{k-1}p, k = \{1,2,3,...\}$.
However, in this question, it seems it is off by 1 since $P(X=1)=0$.
Can someone explain this to me?