Hello, I can say something about that. Sometimes you can use "hayır" or "yok" in some certain situations. Actually, it's not so related to the formal or informal situation. I want to give you some examples. 1) Bu akşam sinemaya gelecek misin? (Will you come to the cinema tonight? ) Hayır, gelmeyeceğim. (No, i won't) Yok, gelmeyeceğim. (No, i won't) In this example, you can use "hayır or yok" By the way it can be rarely considered on the formal or informal situation. 2) Bu kitap hakkında (hiç/any) bilgin var mı? (Do you have any information about this book? Do you know anything about this book? ) Hayır, hiç bilgim yok. (No, i don't have any information about this book.) 3) Burada hiç telefon var mı? (Is there any phone here? ) Hayır, burada hiç telefon yok. (No, there is no phone here.) Note: In some condition, you can use "hayır" or "yok" when you reply to something. "Yok" is also used in some cases. ("Var" is the opposite of the word "Yok" ) 4) Ağaçta kuş var mı ? (Is there a bird on the tree? ) Evet, ağaçta 2 kuş var. (Yes, there are two birds on the tree.) Hayır, ağaçta hiç kuş yok. (No, there isn't any birds on the tree.)

Hello. Sorry I am a bit late and the other answers is good with examples but in terms of linguistics Yok is the Turkish "non-existential clause". Rather than direct negativity as the name implies it expresses a lack of existence... I am giving a weird example here but if you think negatives as negative multiplier in mathematics, using nonexistential is multiplying with zero. There is a slight nuance. Meanwhile "Hayır" is a simple "no".