Schroedinger's crying baby

Suppose you have an infant who naps peacefully for two hours at a time and then wakes up, crying, due to hunger. After eating quickly, the infant plays alone for another hour, and then cries due to tiredness. This cycle repeats several times over the course of a $12$-hour day. (Your rock star baby sleeps peacefully $12$ hours through the night.)

You’re working in an adjacent room when your partner walks out and hands you the baby monitor. You’ve completely lost track where in the day this happens. You continue working for another $30$ minutes, then you hear the baby cry. What’s the probability that your baby is hungry?

Let's assume that by the $12$-hour "day", we mean that there are $4$ consecutive rounds of: (i) waking up from sleep due to hunger, instantaneously eating, then playing for one hour and then (ii) instantaneously falling asleep (what's your secret?) and sleeping for $2$ hours. The only wrinkly is that I suppose after that fourth nap, the baby just wakes up from hunger, instantaneously eats and then magically sleeps $12$ hours until the next "day".

Given that you were only able to sneak in an additional half an hour of work after the baby monitor handoff and that both the sleep and play periods are greater than half an hour in length, there is nothing distinguishing cries for hunger after sleep from cried for sleep after play.

Assuming that one could "lose track where in the day this happens" within the first half hour of the day, which is totally feasible given the new baby, there are an equal number of times when the baby cries for hunger versus cries for sleep. Therefore, the probability that the baby is crying due to hunger after napping is $50\%$.

Of note, this $50\% - 50\%$ answer would remain the same for any amount of work $t \lt 1$ hour, but if you are able sneak in some amount of work $1 \lt t \lt 2$ hours then you know with perfect clarity that the baby is crying. Further, if $t \gt 2$ hours then you know that you have somehow been working all night or that you have missed at least one cry and have a very unhappy baby and/or spouse. I'm not totally sure what to do with the boundaries when $t=1$ or $t=2$: Can your spouse hand you the baby monitor while simultaneously feeding the instantaneously eating baby or putting the instantaneously sleeping baby down for its nap? The potential quantum superpositions literally (milk) bottle the mind!