The symbol between A and B does not render properly on my computer. I see a gray-bordered box with F0 2D inside of it.

I'll assume it's X = |A - B|.

If I understand this correctly, the only way to get a nonzero payoff is to pick the gold and the silver coin, in which case the payoff is 100. That means that we only really care about P(X = 75) and the other probabilities are irrelevant.

The other values are below.

Expected payoff will be .

Strange problem..