Question

Kyle draws one card from a standard deck of 52 cards. What is the probability that he draws an 8 or a diamond?

A.
113


B.
1752


C.
14


D.
413

Answer 1

To calculate the probability that Kyle draws either an 8 or a diamond from a standard deck of 52 cards, we can use the principle of inclusion-exclusion.

1. **Count the total number of favorable outcomes for drawing an 8.**
- There are 4 cards in the deck that are 8s (8♥, 8♦, 8♣, 8♠).

2. **Count the total number of favorable outcomes for drawing a diamond.**
- There are 13 diamonds in the deck (one for each rank).

3. **Count the overlap (the number of cards that are both an 8 and a diamond).**
- There is 1 card that is both an 8 and a diamond (8♦).

4. **Calculate the total number of favorable outcomes using inclusion-exclusion.**
- Total = (Number of 8s) + (Number of diamonds) - (Number of cards that are both)
- Total = 4 + 13 - 1 = 16.

5. **Calculate the probability.**
- The probability \( P \) is the number of favorable outcomes divided by the total number of outcomes in the sample space (52 cards).
- \( P = \frac{16}{52} = \frac{4}{13} \).

Therefore, none of the provided options (A. 113, B. 1752, C. 14, D. 413) represent the correct answer. The final probability is \( \frac{4}{13} \).