Question

A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is either a ten or a king is

• A. $\frac{1}{26}$
• B. $\frac{2}{13}$
• C. $\frac{1}{13}$
• D. $\frac{8}{26}$

Hint:

For mutually exclusive events, simply add the number of favorable outcomes of each event directly.
Always reduce the final fraction to its simplest form to match the given options.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question is based on the classical definition of probability using a standard deck of 52 playing cards.
We need to find the probability of drawing a card that is either a "ten" or a "king".

Step 2: Key Formula or Approach:
The probability of an event $E$ is given by:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
Since drawing a "ten" and drawing a "king" are mutually exclusive events (a single card cannot be both a ten and a king simultaneously), the total number of favorable outcomes is the sum of the individual favorable outcomes.

Step 3: Detailed Explanation:

• Find the total number of possible outcomes in a standard deck of playing cards:
\[ \text{Total cards in the deck, } n(S) = 52 \]

• Determine the number of "ten" cards in the deck:
There are 4 suits in a deck (Hearts, Diamonds, Clubs, Spades), and each suit contains exactly one 10.
\[ \text{Number of tens, } n(T) = 4 \]

• Determine the number of "king" cards in the deck:
Each of the 4 suits contains exactly one King.
\[ \text{Number of kings, } n(K) = 4 \]

• Since these are mutually exclusive events, calculate the total number of favorable outcomes:
\[ \text{Favorable outcomes, } n(T \cup K) = n(T) + n(K) = 4 + 4 = 8 \]

• Compute the probability of drawing either a ten or a king:
\[ P(T \cup K) = \frac{n(T \cup K)}{n(S)} = \frac{8}{52} \]

• Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
\[ P(T \cup K) = \frac{2}{13} \]


Step 4: Final Answer:
The probability that the drawn card is either a ten or a king is $\frac{2}{13}$.