The Truth probability It is believed that the opponent in the discussion can not be more than 90% wrong ...
And that you yourself can never be more than 90% right ...
What is the minimum percentage probability of truth (or lack thereof) in the discussions?
Thanks
 A: Fun question. I assume what is meant is:


*

*At most $90\%$ of your opponent's statements are false.
(Thus, at least $10\%$ are true.)

*At most $90\%$ of your statements are true.
Also, every statement is either true or false, and not both. And you both make approximately the same number of statements.
Then: what is the minimum possible percentage of true statements and maximum possible percentage of true statements?
The minimum percentage is when $0\%$ of your statements are true and $10\%$ of your opponent's are true. In this case, overall, only $5$ percent of all statements are true.
The maximum percentage is when $90\%$ of your statements are true and $100\%$ of your opponent's are true. In this case, overall, $95$ percent of all statements are true.
So we have between $5$ and $95$ percent of statements are true. The wide range is due to the fact that both of your requirements were relatively loose requirements, and only bounded the number of true or false statements on one side.
Addendum. If we don't assume that you and your opponent make the same number of statements, then the minimum is $0$ percent and the maximum is $100$ percent. The minimum is when only you talk, and you only make false statements. The maximum is when only your opponent talks, and she only makes true statements.
