Question

The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:

• A. \( \frac{1}{52} \)
• B. \( \frac{2}{13} \)
• C. \( \frac{4}{13} \)
• D. \( \frac{1}{13} \)

Hint:

When using the addition rule in probability, always check for double counting and subtract any repeated elements.

Answer 1

The Correct Option is C

Step 1: Identifying Favorable Cases 
A standard deck contains 52 cards, consisting of 4 suits: hearts, diamonds, clubs, and spades, each containing 13 cards. 
- Number of diamond cards = \( 13 \) 
- Number of king cards = \( 4 \) 
- The king of diamonds is counted twice in both sets, so we subtract 1 to avoid double counting. 
Step 2: Calculating Probability 
The number of favorable cases: \[ {Total diamonds} + {Total kings} - {King of diamonds} = 13 + 4 - 1 = 16. \] 
Thus, the probability: \[ \frac{16}{52} = \frac{4}{13}. \]