A pack of cards

Playing cards originated in China around 800AD. A version arrived in Europe around the 14th century. In Italy the suits were cups, coins, swords, and sticks.

Use of playing cards spread from Italy to Germany and the Latin suits were replaced with leaves, hearts, bells, and acorns.

In France these changed again to clovers, tiles, hearts, and pikes around 1480.

In English, the French suits are called clubs, diamonds, hearts and spades. Here is a complete pack of cards.

There are 13 cards in each suit, making 52 cards in the pack.

Let’s look at choosing cards from the pack at random in order to describe probability. When something is chosen at random then each item has an equal probability of being chosen.

If all the cards were well shuffled and face down and you were to pick a card at random, what is the probability that the card will be a spade?

There are 52 cards and 13 spades so the probability is $\frac{13}{52}$ . If we divide the numerator and denominator by 13 then this simplifies to $\frac{1}{4}$ .

What is the probability of picking either a jack, a queen or a king of any suit if you pick one card at random from the shuffled, face down cards?

There is a jack, queen and king in each suit

Twelve of the cards are jacks, queens or kings so the probability of picking one is $\frac{12}{52}$ . If we divide the numerator and denominator by 4 then this simplifies to $\frac{3}{13}$ .

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Probability

A pack of cards