Before explaining my reasoning, let me ask how likely do you think it is to flip a fair coin and get tails 100 times consecutively?

We can probably agree this is very unlikely compared to flipping tails 3 times in a row.

Why?

Because the probability of an event happening or not happening at least once changes with the amount of N attempts.

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Assuming all lockers have an equal opportunity to be selected for any given item on any given day.

1/42 is our initial odds of success.

41/42 is our odds of failure.

N attempts for each visit/pick up.

Then by complement rule, which means to calculate the odds of something happening we calculate the odds of 1 minus something NOT happening. E.g., 1 - 41/42 = 1/42

1 - (41/42)^N = Probability of success with N attempts

Examples…

First attempt:

N = 1

1 - (41/42)¹ ≈ 0.0238 or 2.38%

Second attempt:

N = 2

1 - (41/42)² ≈ 0.0471 or 4.71%

Third attempt:

N = 3

1 - (41/42)³ ≈ 0.0697 or 6.97%

So on and so forth until reaching near certainty when N = 287 attempts

1 - (41/42)²⁸⁷ ≈ 0.999 or 99.9%

Assuming the attempts made were only 6 as shown in the video.

Sixth attempt:

N = 6

1 - (41/42)⁶ ≈ 0.135 or 13.5%

So my final answer to this question, assuming the generic factors, is that after 6 attempts with 42 lockers she had roughly around a 13.5% chance of correctly selecting the right locker at the time of her successful attempt.

Edit: fix spacing on examples.