Two ways to look at it.  The nonmathematical way:

"One-half the cards are red, so the probability is one-half".  That's because
one-half of the time you'll get a red card and the other half of the time you
won't.

The mathematical way.  There are 26 red cards in a deck of 52.  So the
probability of getting a red card is 26 ways out of 52, or 26/52 which reduces
to 1/2.

Edwin