Answer: 13/51
Step-by-step explanation: After shuffling there are 52 permutations of 52 cards. Each has the probability of occurrence equal to another, that is the probability of any sequence of cards is 1/52.
Let's count only those where there is a red card on the first place and black card on the second. There are 26 red and 26 black cards. Therefore, we have 26 ⋅26 choices for a pair of two first cards. The sequence of other 50 cards in unimportant and any permutation among them is fine for us since we fixed the first two.
Therefore, we have 26 ⋅ 26 ⋅50 different permutations when the first card is red and the second is black.
Therefore, we have 26 ⋅ 26 ⋅50 different permutations when the first card is red and the second is black.
The final probability, therefore, is
26 ⋅26 ⋅50 / 52 = 26 ⋅26 / 52 ⋅ 51 = 13 / 51
13/51 is the final answer
