# When picking a random card from a standard deck, what is the probability of drawing a card that is less than a 10 (and so not K, Q, J, 10)?

For a standard 52 card deck it's $\frac{9}{13}$. Add the 2 jokers to make 54 cards and it's $\frac{2}{3}$.

#### Explanation:

A standard deck has 52 cards, so I'll answer first for 52 and then since the question has 54 as the question, I'll add in the 2 extra cards (I'll presume these to be jokers).

52 cards

Within a standard deck, there are 13 ordinal cards (Ace, or 1, through 10, and then Jack, Queen, King) with each ordinal having 4 suits: spades, hearts, diamonds, clubs. $13 \times 4 = 52$

For the probability of picking a card less than 10, we're looking for cards 1 through 9 in each of the 4 suits: $9 \times 4 = 36$

The number of cards we can pick from is 52, and so the probability is:

$\frac{36}{52} = \frac{9}{13}$

54 cards

If we add the 2 jokers, we end up with $\frac{36}{54} = \frac{18}{27} = \frac{2}{3}$