When drawing a card randomly from a deck what is the probability that it will be either a heart or a one-eyed jack?

The probability of drawing a heart is 1/4 or 25% (i.e., 13 of 52 cards).

According to Wikipedia*, the one-eyed jacks are jack of spades and jack of hearts. The probability of drawing jack of spades is 1/52 (one card of 52).

Therefore drawing either a heart (including the jack of hearts) OR jack of spades is (13/52 + 1/52)

= 14/52

= 7/26

= 0.269

Just under 27 percent.

* http://en.wikipedia.org/wiki/One-eyed_jack#One-eyed_Royals