Is "In each observation, the chance that sth. was provided was x %" a clear description of a controlled experiment?

Question

I ran a controlled experiment and am now trying to explain the conditions I investigated. In one condition, the chance that the subjects in my study got some additional information Z for a specific item was 20%. I first wrote

Z was provided at a random chance of 20%.

My institute employs an English native speaker for proofreading our writing. She told me to replace "at a random chance of 20%" with "in a random 20% of cases". However, I think this is not exactly what I am trying to express, but I cannot ask her at the weekend and have a very close deadline for this text.

The problem with her suggestion is that (please correct me if I am misunderstanding this) it means that the subjects got Z for exactly 20% of the items. What I am trying to say is: For each combination of subject and item, the chance that Z was provided was 20%. So some subjects actually got Z for less than 20% of the items, whereas others got it for more than 20%. Based on this answer, I came up with this sentence now:

In each observation, the chance that Z was provided was 20%.

Does this express what I am trying to say?

Answer 1

In your opening you state

the chance that the subjects in my study got some additional information Z for a specific item was 20%

This is almost what I would write. Specifically I would suggest

For each item participants were assigned Z with probability 0.2

In the environment I work in (health) subjects is usually avoided in favour of a word like participants or, if they are ill, patients. It may be OK for you though.