Questions: A single card is drawn from a standard deck of 52 cards. What are the odds against drawing an even numbered card?

Transcript text: A single card is drawn from a standard deck of 52 cards. What are the odds against drawing an even numbered card? $\square$ : Enter your result in lowest terms (remove common factors)

Solution

Solution Steps

To find the odds against drawing an even numbered card, first determine the total number of even numbered cards in a standard deck. Then, calculate the odds against by comparing the number of non-even cards to even cards.

Step 1: Determine Total Even and Non-Even Cards

In a standard deck of 52 cards, the even numbered cards are 2, 4, 6, 8, and 10, which appear in each of the 4 suits. Thus, the total number of even cards is: \[ \text{Total Even Cards} = 5 \times 4 = 20 \] The number of non-even cards is: \[ \text{Non-Even Cards} = 52 - 20 = 32 \]

Step 2: Calculate Odds Against Drawing an Even Card

The odds against drawing an even numbered card can be expressed as the ratio of non-even cards to even cards: \[ \text{Odds Against} = \frac{\text{Non-Even Cards}}{\text{Even Cards}} = \frac{32}{20} \]

Step 3: Simplify the Odds

To express the odds in lowest terms, we simplify the fraction: \[ \frac{32}{20} = \frac{8}{5} \]