# If you a draw a card from a standard deck of 52 cards, what is the probability that the card will be an odd number?

If the Ace isn't odd, $\frac{4}{13}$. If the Ace is odd, $\frac{5}{13}$

#### Explanation:

In a standard deck of cards, there are 13 ordinals: 9 numbered cards 2-10, plus cards Jack, Queen, King, and Ace (which could be considered a 1). There is one of each ordinal in each of four suits: clubs, spades, hearts, diamonds.

The calculation then rests on whether we consider the Ace an odd card or not. I'll do the calculation both ways.

Ace is not odd

The ordinals 3, 5, 7, and 9 are odd. There are four of each (one for each suit) and so $4 \times 4 = 16$ odd cards. This makes the probability:

$P \left(\text{draw an odd card}\right) = \frac{16}{52} = \frac{4}{13}$

Ace is odd

If we want to consider the Ace as a 1, then there are 5 ordinals that are odd, $5 \times 4 = 20$ odd cards, and therefore:

$P \left(\text{draw an odd card}\right) = \frac{20}{52} = \frac{5}{13}$