The standard deck of cards contains a total of 52 cards, in which, 26 cards are red and 26 cards are black.
In order to have more red cards than black cards, there should be at least 7 red cards among 13 cards.
Let X be the number of red cards out of 13 cards. So, the required probability that there are more red cards than black cards is given by P(X $\ge $ 7).
Since the cards are picked without replacement, we use combinations (hypergeometric distribution) to find the probability.
The probability can be calculated as follows: