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: Use one suit as a representative sample instead of the full deck.
A standard deck is made of 4 identical suits, each with 13 cards, so the proportion of favourable cards is the same in every suit.
Step 2: Count favourable cards within a single suit.
In any one suit of 13 cards, exactly one card is a ten and exactly one is a king, so 2 out of 13 cards are favourable.
Step 3: Carry that proportion over to the whole deck.
Since the ratio is identical in every suit, the probability for the full deck is also $\frac{2}{13}$, without needing to add $\frac{4+4}{52}$ separately.
\[ \boxed{\frac{2}{13}} \]