A TRACON Controller providing OJT instruction reported their trainee did not notice an unidentified VFR aircraft was in confliction with a descending aircraft resulting in a NMAC.

Narrative

I was the OJTI training on sector 2. Traffic was not complex or busy. I saw the VFR aircraft at 6;500' 20 miles southeast of the incident. I didn't say anything because I had already inserted myself several times into prior situations where the trainee had indicated (either verbally or physically) that they were just about to 'do that'. I wanted the trainee to see things himself and see if they responded appropriately. In this instance; where I would have normally inserted a correction or asked the question 'Do you see that VFR at 6;500''; I got distracted by an equipment malfunction. Progress strips seemed to have stopped printing on departures from ZZZ. To evaluate whether it was a one time issue; just our sectors issue or a bigger issue I walked a few scopes down to the CIC to discuss the issue. By the time I came back; my trainee said to me 'I had an RA'. I didn't think much of it since Aircraft X was at 7;000' by the time I was there and the trainee told me about it I had assumed (incorrectly) that Aircraft X descended to 6;800' or so and climbed back up. I was not told they were at the same altitude.The Aircraft X pilots response was 'that was a close one'. I assumed incorrectly that 300' was close for him (and I agree) and I was unaware they were at the same altitude. This was the trainees 3rd instance of almost climbing into VFR aircraft in the last 2 days. The prior 2 I had to ask 'do you see the VFR?' and their response was 'no'. This was all due to an equipment malfunction that distracted me - I've never let this happen before.I recommend prohibiting controllers from tagging up aircraft that are not radar identified and being talked to. I notice a trend of controllers (and trainees) becoming over-reliant on someone's 'benevolence' of putting a radar tag on a VFR 1200 code aircraft and making it yellow to the entire room. This has created a dependence upon seeing only tagged aircraft whereas what has really happened is controllers stop scanning for VFR aircraft as they are supposed to. Let's not rely on memory aids that are inconsistent but rather our given brains to scan and do our jobs with excellence.