Let us suppose at present
1 dollar = 1 euro
After 1 year
There is 50% chance that 1 dollar = .80 euro ...[1]
And there is 50 % chance that 1 dollar = 1.25 euro ...[2]
Therefore expected value of 1 dollar after 1 year = .5*.8+.5*1.25 = 1.025 euro ...[a]
But statement 1 and 2 can be written as
There is 50% chance that 1 euro = 1.25 dollar ...[3]
And there is 50 % chance that 1 euro = .8 dollar ...[4]
Therefore expected value of 1 euro after 1 year = .5*.8+.5*1.25 = 1.025 dollar ...[b]
But statement [a] and [b] cannot be both right.
What is wrong here?
I don't know if this fits here? But this riddle was posed in this stat lecture https://youtu.be/UZjlBQbV1KU?list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo