Foreign Exchange Fallacy

Question

Suppose that:

1. \$1 is worth €1 now;
2. For next year, there's 50% chance that \$1 is worth €1.25 and 50% chance that \$1 is worth €0.8.

Then the expected value of \$1 in terms of euros is 1.025. However, the expected value of €1 in terms of dollars is also 1.025. This seems to be saying that dollar is expected to be both appreciating and depreciating. How is it even possible?