The woman might know the strange events,____(不是吗）？

显然是用doesn't she? 因为在这个里面.might是情态动词,表示猜测的.所以may / might / must / can’t / couldn’t 表猜测时的反意疑问句。
He might have a lot of work to do now , doesn’t he ?
He may have missed the early bus , hasn’t he ?
I must have been asleep when you rang me , wasn’t I ?
It can’t rain tomorrow , will it ?
He must be studying in the classroom now , isn’t he ?

陈述句中谓语动词是may / might 时，反意疑问句用mayn’t / mightn’t构成。E.g. I may come and borrow your bike tomorrow, mayn’t I? The experience may have been long in your memory, mayn’t it?

只个里面,may/might是助动词

反意疑问句用法种种

1. 当陈述句的主语为anybody, anyone, everybody, everyone, somebody, someone, nobody, no one, these, those时，反意疑问句的主语用they。E.g. everybody knows what I said, don’t they? Nobody says a word about the incident, don’t they? Somebody borrowed your bike yesterday, didn’t they? Anybody can do it, can’t they?
2. 当陈述句的主语为this, that, everything, anything, nothing, something等时，反意疑问句的主语用it。E.g. Eve