What is the public safety exception to the Miranda requirement?

As you've learned in other cards, generally speaking, a detainee must be read their Miranda rights before a custodial interrogation takes place. However, like most things in the legal world, there are sometimes exceptions. One such exception is public safety. The best way to explain this is to talk about the case it comes from, New York v. Quarles:

In 1984, a couple of police were driving down the street in New York when they were approached by a woman who claimed that she had just been raped by an armed man. She described the man and said he had run into a local supermarket. One of the officers ran into the supermarket and was able to identify a suspect matching the victim's description. The officer drew his weapon on the suspect and demanded he show his hands. The suspect ran away, deeper into the supermarket. The officer chased after him but briefly lost him. After finding the suspect again, the officer handcuffed him and searched him for a gun. The officer found no gun, but did find an empty gun holster.

It was at this point that the officer demanded the suspect tell him where the gun was. The officer's fear was that the gun would be accidentally discovered by one of the store's customers and possibly cause harm. The suspect told the officer where he had hid the gun, and the officer was able to secure it, then the officer read the suspect his Miranda rights. Later, during trial, when the gun was entered as evidence against the suspect, his attorneys were able to suppress it based on the fact that suspect had not yet been Mirandized when the officer, who had handcuffed him, demanded to know where the gun was.

Technically the suspect was in custody, and technically the officer's demands to know where the gun was does qualify as an interrogation, so under the general Miranda rule, this would require that the evidence be thrown out since he had not yet been read his rights. However, the SCOTUS held that in these specific circumstances where there is a legitimate concern for public safety, the law will be a little forgiving of officers who—in the heat of the moment of trying to protect the public—obtain otherwise inadmissible statements because they forgot to first Mirandize the defendant.

As you can see, this is a super fact-specific, unique circumstance that would require the fact pattern in your exam to illustrate some imminent, dangerous situation to the public.