The probability that Docter Probs succeeds on a single surgery, which is independent from other surgeries, is $p$. Every time he performs 3 successful surgeries in a row, he shouts 'yay!'. Specifically, say if he performs 6 successful surgeries in a row, then he shouts 'yay' 4 times.
How many 'yay!'s is he expected to shout if he performs 100 surgeries in a row?
Here's what I've tried so far: The probability of any 3 surgeries in a row being successful is $p^3$. In 100 surgeries, he can have a maximum of 98 'yays!'. Hence, he will shout $98p^3$ 'yays!'.
However, I just realized that the probabilities of shouting yays are not independent. How do I take into account how one failed surgery could affect up to 3 yays?