Question

One card is drawn from a pack of $52$ cards. The probability that it is a king or diamond is

• A. $\frac{1}{26}$
• B. $\frac{3}{26}$
• C. $\frac{4}{13}$
• D. $\frac{3}{13}$

Answer 1

The correct option is C

$\frac{4}{13}$

Explanation for the correct option:

Finding the probability:

Total number of cards are $52$.

Total diamond cards are $13$ and there are $4$ kings, therefore total card is $(13+4)=17$

Since we have one of the king belonging to diamond, we subtract one from the total, to avoid double counting.

Therefore, total number of favorable cards is $(17-1)=16$.

So, required probability is the ratio total number of diamond or king cards to the total number of cards in a deck so,

$$\begin{gathered} P=\frac{\text{Favorable outcome}}{\text{Total Outcome}} \\ =\frac{16}{52} \\ =\frac{4}{13} \end{gathered}$$

Hence, the correct answer is option (C).