Find the number of times an even number is followed by an odd for 10 fair dice rolls.
Easy to see that for two dice rolls the probability of an even number being followed by an odd is $\frac{1}{4}$ .
And "find the number of times" usually indicates that we have to use indicator functions. But I just cant come up with the right idea behind formulating the indicator random variable for which I think I need to take the conditional expectation.
Is it the type of question where you have to consider the $k$th and $k+1$ rolls? Any hints or ideas are appreciated!