A standard 52-card deck has four 13-card suits: diamonds, hearts, clubs, and spades. The diamonds and hearts are red, and the clubs and spades are black. Each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king, and an ace. An experiment consists of drawing 1 card from the standard deck. Find the probability of drawing a black nine of diamonds.
The probability of choosing a black nine of diamonds is (Type an integer or a simplified fraction.)
The correct answer and explanation is :
To find the probability of drawing a black nine of diamonds from a standard 52-card deck, we need to first understand what this means.
Step 1: Understand the deck
A standard deck of 52 cards has:
- 4 suits: hearts, diamonds, clubs, and spades.
- Each suit has 13 cards: Ace, 2 through 10, Jack, Queen, King.
- Hearts and diamonds are red.
- Clubs and spades are black.
Step 2: Analyze the card in question
You are asked for the probability of drawing a black nine of diamonds.
- The nine of diamonds is part of the diamonds suit.
- But diamonds are red, not black.
So, the nine of diamonds is a red card.
This means that a black nine of diamonds does not exist in a standard 52-card deck.
Step 3: Conclusion
Since such a card does not exist in the deck, there are zero favorable outcomes for drawing a black nine of diamonds.
- Total possible outcomes (cards in the deck): 52
- Favorable outcomes (black nine of diamonds): 0
Final Answer:
[
\text{Probability} = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{0}{52} = 0
]
Detailed Explanation (300+ words):
Probability is the measure of the likelihood that an event will occur, expressed as a fraction:
[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
]
In this experiment, one card is drawn at random from a standard deck of 52 cards. The suits are diamonds, hearts, clubs, and spades, each with 13 cards. Among these, diamonds and hearts are red, while clubs and spades are black.
We are asked to find the probability of drawing a black nine of diamonds. To determine this, we first analyze whether such a card even exists.
- The nine of diamonds belongs to the diamonds suit.
- All diamond cards are red by definition.
- Therefore, the nine of diamonds is red.
Saying “black nine of diamonds” is a contradiction—like asking for a square circle. The card does not exist in the deck. Because of this, there are zero favorable outcomes for the event. There are still 52 possible outcomes since any one of the 52 cards might be drawn.
This leads to:
[
\text{Probability} = \frac{0}{52} = 0
]
Hence, the probability of drawing a black nine of diamonds is 0 because such a card is not part of the standard deck.