Correlation between radiological sign and clinical symptom: choosing the test

I'm new to the forum and very rusty on statistics. I'm studying to learn enough autonomy, but I really can use some of your kind help :)

A group of patients (age known for each) are referred to the radiologists because of hip pain. The clinician suspects X. The radiologist finds out that among these patients:
group a had X
group b had Y
group c had X+Y
group d had none of the above

We feel very strongly that is a correlation between the unexpected Y finding and the hip pain that started the diagnostic process. We want to highlight how patients in group b had Y alone and not X.

What would you suggest as the best statistical method to test that hypothesis?
Secondarily, how should I correlate the findings with the age groups?

I thank you in advance for any instructions you are willing to give.