In which ways do anagamis still experience ignorance? According to the ten fetters model, one of the five fetters which are only removed at attaining arahantship is ignorance (avijja). This means that anagamis are still subject to ignorance in some way. But it's also evident that anagamis possess a lot less ignorance than ordinary people. For example, belief in a self (sakkaya-ditthi) is abandoned at the first stage of enlightenment. So which forms of ignorance would an anagami still experience, and which forms not? Or is ignorance something that only sometimes arises in an anagami, the same way ill-will is only sometimes present in ordinary people?

Thanks in advance for your answers!
According to MN 9 (below), as long as you still have fermentation or effluents, you would still have ignorance, and vice versa (also see this question). Ignorance is a very deeply ingrained and deeply lingering fetter.


  From the origination of fermentation comes the origination of
  ignorance. From the cessation of fermentation comes the cessation of
  ignorance. .....
  
  From the origination of ignorance comes the origination of
  fermentation. From the cessation of ignorance comes the cessation of
  fermentation.


There is a vicious cycle between ignorance and fermentation.

There seems to be four types of fermentations in the Dhammawiki page of fermentation:


  
  The mental fermentation of sense-desire (kāmāsava), Ex: 'All is pleasant'
  The mental fermentation of desiring existence (bhavāsava), Ex: 'Being is good'
  The mental fermentation of wrong views (ditthāsava), Ex: 'My opinion is best'
  The mental fermentation of ignorance (avijjāsava). Ex: 'Suffering exists not'
  


According to this wikipedia page on ten fetters, the Anagami still has the fetters of lust for material existence, lust for immaterial existence, conceit, restlessness and ignorance.

So, the Anagami would have overcome the mental fermentation of sense-desire (kāmāsava) and the mental fermentation of wrong views (ditthāsava). However, he would still be challenged by the mental fermentation of desiring existence (bhavāsava). I take it that conceit is related to bhavāsava.

What does this mean?

The Anagami has overcome self-view, attachment to rituals, doubt, sensual desire and ill will. But the Anagami still has the mental fermentation of wanting to exist. And this will cause ignorance to continue.

You know the Four Noble Truths very well, dispelled wrong views (including self-view), overcame sensual desire and overcame ill will. But when someone threatens your life, you may get scared. Why? It's because you still want to exist.