In this case, the many to many relationships
should be obvious, but I feel I must point out:
Based on that text specifically, all that's needed is that the patient and hospital each have a doctor ID column. How many would get it if you specifically pointed out that they need to consider real-world circumstances in this, and / or if you enumerated all the requirements?
Many many many times, when stating a hypothetical question, real-world handling responses are not desirable to the questioners. If the interviewee realizes this, they also realize that they risk losing points no matter how they answer: answering based on the specified requirements fails with you, but answering based on real-world uses fails with people testing against over-engineering / people religious about specific answers to specific questions. And being verbose risks both groups, based pretty much solely on the interviewer, of whom they have effectively no knowledge.
Or have you done this, and it just wasn't included in the example above?