A deck of playing cards contains 52 cards, including 4 aces. If one card is drawn at random from the deck, what is the probability of drawing an ace?
The Correct Answer and Explanation is :
Probability of Drawing an Ace from a Deck of 52 Cards
In a standard deck of 52 playing cards, there are 4 aces (Ace of Spades, Ace of Hearts, Ace of Diamonds, and Ace of Clubs). When a card is drawn randomly from the deck, the probability of drawing an ace can be calculated using the basic probability formula:
[
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
]
Here:
- Number of favorable outcomes (drawing an ace) = 4
- Total number of possible outcomes (total cards in the deck) = 52
[
P(\text{Ace}) = \frac{4}{52}
]
Simplifying the fraction:
[
P(\text{Ace}) = \frac{1}{13} \approx 0.0769 \text{ or } 7.69\%
]
Explanation
- Understanding Probability
Probability is the measure of how likely an event is to occur. It is expressed as a fraction, decimal, or percentage, ranging from 0 (impossible) to 1 (certain). - Total and Favorable Outcomes
Since a deck consists of 52 unique cards, and only 4 of them are aces, the probability of drawing an ace is calculated as the ratio of these two numbers. - Simplifying the Probability
The fraction (\frac{4}{52}) simplifies to (\frac{1}{13}), making it easier to interpret. - Real-Life Relevance
In card games like poker or blackjack, knowing the probability of drawing an ace can help in decision-making. Since the chance is only 7.69%, drawing an ace on the first attempt is unlikely.
Now, I will generate an image representing this probability visually.
Here is the generated image visually representing the probability of drawing an ace from a deck of 52 cards. Let me know if you need any modifications or further explanations!