Third toy of one type before second of another

Two independent machines run nonstop: one makes spinning tops and the other makes action figures. Each toy takes an $\text{Exp}(1)$ amount of time, independent of everything else, and each machine starts its next toy immediately after finishing one. What is the probability that the third spinning top is completed before the second action figure?

$5/16$. By memorylessness and equal rates, each completed toy is equally likely to come from either machine, independently, so the sequence of completions is like fair coin flips. We need at least $3$ tops among the first $4$ completions: $\tfrac{4+1}{16}=\tfrac{5}{16}$.