Suppose we are playing a modified version of the Zener card guessing game, except this time we only have 4 kinds of cards (circle, cross wave, square) with five cards per type, in a pack of 20 total cards (call it a deck). In the guessing game, person A shuffles the deck, draws a single card, records the card, has person B say their guess, discards the card and shuffles the deck again. My question is, what is the probability of guessing 2 cards correctly.
So far, I understand that the probability of guessing a single card would be $\frac{5}{20}$ since there are 5 of each card and there's a total of 20. My issue is with interpreting the problem without replacement for more than one guess. I have setup my conditional probability as such: P($G_1$$\cap$$G_2$) = P($G_1$)P($G_2$|$G_1$), where $G_1$ and $G_2$ are the guesses. We already know P($G_1$) to be $\frac{5}{20}$, however, I am uncertain if P($G_2$|$G_1$) = $\frac{4}{19}$ since the next card could be from a different set of symbols. It would make sense if we were talking about a standard 52 deck of playing cards with suits and faces but I'm not sure if we can apply the same reasoning. Thanks for the help