probability that the second card drawnks an
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![**Probability of Drawing an Ace: A Card Probability Problem**
*Educational Exercise: Understanding Conditional Probability in Card Drawing*
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**Problem Statement:**
In a standard 52-card deck, the first card randomly drawn is an ace. If the ace is not put back into the deck, what is the probability that the second card drawn is an ace?
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**Options:**
A. 3/52
B. 4/52
C. 3/51
D. 4/51
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**Detailed Analysis:**
The right side of the image displays all 52 cards arranged in four rows, one for each suit: Hearts, Diamonds, Clubs, and Spades. Each row consists of 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
To solve the problem, we need to consider the following points:
1. **Total Cards Initially**: 52 cards.
2. **Aces in the Deck**: There are 4 Aces in a full deck.
3. **First Card Drawn is an Ace**: If one ace is already drawn and not replaced, there are 51 cards left in the deck.
4. **Aces Remaining After First Draw**: After drawing one Ace, 3 Aces remain in the 51 cards.
**Probability Calculation:**
- **Remaining Aces**: 3
- **Remaining Total Cards**: 51
- The probability of drawing one of the remaining Aces is:
\[ \frac{3}{51} = \frac{1}{17} \]
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**Answer:**
The correct answer is
**C. 3/51**
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