An ace, 10 of diamonds, or 2 of spades appears in drawing a single card from a well-shuffled ordinary deck of 52 cards.
The correct answer and explanation is :
To find the probability of drawing an ace, a 10 of diamonds, or a 2 of spades from a standard deck of 52 cards, we follow these steps:
Step 1: Count Favorable Outcomes
- There are 4 aces (one in each suit: hearts, diamonds, clubs, and spades).
- There is 1 ten of diamonds.
- There is 1 two of spades.
Since these events are mutually exclusive (they do not overlap), we simply add their probabilities.
Step 2: Compute Probability
The probability of drawing an ace:
[
P(Ace) = \frac{4}{52}
]
The probability of drawing a 10 of diamonds:
[
P(10\ of\ Diamonds) = \frac{1}{52}
]
The probability of drawing a 2 of spades:
[
P(2\ of\ Spades) = \frac{1}{52}
]
Adding these probabilities together:
[
P(Ace\ or\ 10\ of\ Diamonds\ or\ 2\ of\ Spades) = \frac{4}{52} + \frac{1}{52} + \frac{1}{52} = \frac{6}{52}
]
[
= \frac{3}{26} \approx 0.1154 \text{ (or 11.54%)}
]
Explanation
The probability calculation is straightforward since the three outcomes (drawing an ace, a 10 of diamonds, or a 2 of spades) do not overlap. If they did, we would have to subtract their intersection. However, each card is unique, so their probabilities add directly.
This method applies the addition rule of probability, which states that for mutually exclusive events, the probability of one occurring is the sum of their individual probabilities.
Thus, the probability of drawing an ace, a 10 of diamonds, or a 2 of spades from a standard deck of 52 cards is 3/26 or 11.54%.
Here is the image generated using DALL·E, OpenAI’s legacy image-generation model. It visually represents the probability question with a deck of 52 cards spread out, highlighting the Ace of Spades, 10 of Diamonds, and 2 of Spades on a green felt poker table.