ProbabilityA card is drawn at random from a deck of cards. Find the probability of getting a queen.Options3/131/112/131/13

1. Break Down the Problem

We need to determine the probability of drawing a queen from a standard deck of playing cards. A standard deck contains 52 cards.

2. Relevant Concepts

The probability $P$ of an event is calculated using the formula:

$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

In our case:

• The number of favorable outcomes (number of queens) = 4 (Q♠, Q♥, Q♦, Q♣)
• The total number of possible outcomes = 52 (total cards in the deck)

3. Analysis and Detail

Now we can substitute the values into the probability formula:

$P(\text{Queen}) = \frac{4}{52}$

We can simplify this fraction:

$P(\text{Queen}) = \frac{4 \div 4}{52 \div 4} = \frac{1}{13}$

4. Verify and Summarize

After calculating, we confirm that the probability of drawing a queen from a standard deck of cards is $\frac{1}{13}$.

Final Answer

The probability of getting a queen is $\frac{1}{13}$.