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: Find the probability of each event separately.
A deck has 52 cards with 4 tens and 4 kings. So $P(\text{ten}) = \frac{4}{52}$ and $P(\text{king}) = \frac{4}{52}$.
Step 2: Add the probabilities since the events cannot happen together.
A single card cannot be both a ten and a king, so these are mutually exclusive events, and by the addition rule $P(\text{ten or king}) = P(\text{ten}) + P(\text{king}) = \frac{4}{52} + \frac{4}{52}$.
Step 3: Simplify the sum.
This gives $\frac{8}{52}$, which reduces by dividing top and bottom by 4 to $\frac{2}{13}$.
\[ \boxed{\frac{2}{13}} \]