If you pick one normal playing card from a deck at random, what's the probability that it will be a Jack, Queen, King, or heart? O.K. to leave answer in fractional form.

To solve this probability puzzle, we need to count the "favorable" cards without double-counting any. A standard 52-card deck contains 12 face cards (the Jack, Queen, and King of each of the four suits). The deck also has 13 hearts. A common pitfall is to simply add 12 and 13 to get 25. The problem is that three of those cards—the Jack of hearts, Queen of hearts, and King of hearts—belong to both groups. They are both face cards and hearts.

To find the correct total, we must add the two groups and then subtract the overlap. This gives us 12 face cards plus 13 hearts, minus the 3 cards they have in common, which equals 22 unique cards. This calculation demonstrates a key concept in probability called the inclusion-exclusion principle. Since there are 52 total cards in the deck, the chance of drawing one of these 22 specific cards is 22 out of 52. This fraction can be simplified by dividing both the numerator and the denominator by 2, giving us the final probability.