Why is B appearing so often with this randomizer?

I see greater variation with a shorter interval - for instance, 0.2

pyglet.clock.schedule_interval(refresh, 0.2)

since each label stays visible less time.

Your pick in schedule_interval() has a problem - you get NameError: name 'pick' is not defined since pick exists locally within refresh() and isn't available beyond that function.

This example won't run since the variable pick isn't in the scope containing the invocation of pyglet.clock.schedule_interval

What you intend isn't clear. Should the interval really differ from one execution of this program to another? Keeping the interval constant seems more reasonable.

Reorganizing things could help.

The runtime behavior seems a little strange, although that could simply be something about pyglet or my limited understanding of it. Regardless, this alternates between showing "Press A" and "Press B" at a pseudo-random rate.

from random import SystemRandom
from pyglet import window, text, clock, app

# pylint: disable=possibly-used-before-assignment,unused-argument

# note use of variable names in uppercase denoting global scope

TICK_SECONDS = 3.

def refresh(elapsed: float) -> None:
    SCREEN.clear()
    RNG.choice(CAPTIONS).draw()

if __name__ == "__main__":
    SCREEN = window.Window(fullscreen=True)
    label_options = {  # these parameters are common to both captions
        "font_name": "Times New Roman",
        "font_size": 72,
        "x": SCREEN.width // 2,
        "y": SCREEN.height // 2,
        "anchor_x": "center",
        "anchor_y": "center",
    }
    # create a tuple of the 2 captions
    CAPTIONS = text.Label("Press A", **label_options), text.Label("Press B", **label_options)
    RNG = SystemRandom()  # only do this once
    clock.schedule_interval(refresh, TICK_SECONDS)
    app.run()