A deck of cards has 52 cards. There are 4 suits, diamonds, hearts, clubs
and spades. Each suit has 13 cards.
What is the probability that I will
randomly pick a King?

There are 52 cards in total. 13 of them are spades and 4 of them are two’s. At first hand you might think that there are 13+4=17 cards that can be marked as “spade or two" but counting like that card “spade 2” is counted twice. Repairing this we find that there are exactly 13+4-1=16 cards that can be marked as “spade or two". We call this an application of the principle of inclusion/exclusion.

Then applying the rule that probability equals number of favourable outcomes divided by number of possible outcomes we find that the probability on drawing such card equals:

16/52=4/13.