Expected Values Gone Right or Wrong?
I have 52 cards in a standard deck. I draw a card and label it as f(1). Let the value of f(1) = the numerical value of the card. If f(1) is a face card, f(1) = 0 and if f(1) is an ace, f(1) = 11. Suppose I draw 10 cards with replacement, value of (E[f(x)])^2 where f(x) = the summation from Z = 1 to 10 of f(Z) can be expressed in the form of A/B where A and B are co-prime integers. Find the value of A+B.