Question

Calculate the theoretical probability of choosing an even-numbered card from a traditional deck of 52 cards. For this question, face cards are not counted as odd or even. Simplify.(1 point)
Responses


Start Fraction 7 over 13 End Fraction


Start Fraction 5 over 13 End Fraction


Start Fraction 4 over 13 End Fraction
20/52

Answer 1

In a traditional deck of 52 cards, the even-numbered cards are 2, 4, 6, 8, and 10. Each of the four suits (hearts, diamonds, clubs, spades) has one of each of these cards.

Let's calculate the total number of even-numbered cards:

- 2 of hearts
- 2 of diamonds
- 2 of clubs
- 2 of spades

Total for the number 2 = 4 cards

- 4 of hearts
- 4 of diamonds
- 4 of clubs
- 4 of spades

Total for the number 4 = 4 cards

- 6 of hearts
- 6 of diamonds
- 6 of clubs
- 6 of spades

Total for the number 6 = 4 cards

- 8 of hearts
- 8 of diamonds
- 8 of clubs
- 8 of spades

Total for the number 8 = 4 cards

- 10 of hearts
- 10 of diamonds
- 10 of clubs
- 10 of spades

Total for the number 10 = 4 cards

Now, summing all even-numbered cards:
\[ 4 (from \: 2) + 4 (from \: 4) + 4 (from \: 6) + 4 (from \: 8) + 4 (from \: 10) = 20 \: even \: cards. \]

Next, the probability of selecting one of these even-numbered cards from a full deck of 52 cards is given by the formula:
\[
P(\text{even-numbered card}) = \frac{\text{Number of even cards}}{\text{Total number of cards}} = \frac{20}{52} = \frac{5}{13} \: \text{(after simplifying)}.
\]

Thus, the theoretical probability of choosing an even-numbered card from a traditional deck of 52 cards is:
\[
\frac{5}{13}.
\]

The correct response is:
**Start Fraction 5 over 13 End Fraction**.