Just to address the other answer, the epiglottis prevents food from entering your trachea. It doesn't help direct air between your mouth and nose. It is not anywhere near the right location to do that.

The palate and tongue can make a seal that blocks off the mouth, forcing all air to move through your nose (even when your mouth is open).

The soft palate can't fully block off the nasopharynx in normal people, so there's always at least some air coming through the nose, but with a wide-open mouth and lifted soft palate, chances are more air is going to move through the mouth.

In [1], when subjects were not exercising, some breathed only through their noses, while others breathed partly through their mouths; however, even in the mouth breathers, 70% of the air came through their noses. When the subjects were exercising hard, everyone used their mouth. The proportion of air passing through the mouth reached 70% in habitual "mouth breathers" but only 60% in habitual nose breathers. This is probably because people who habitually breathe through their mouths have higher nasal resistance.

[1] Niinimaa et al., "Oronasal distribution of respiratory airflow" (1981), https://pubmed.ncbi.nlm.nih.gov/7244427/