Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probability of the second card, given the information about the removed card provided. (Enter the probability as a fraction.)
P(ace|five)

To find the probability of drawing an ace given that a five was drawn first and removed, let's break down the problem:

1. **Total number of cards in a standard deck:** 52
2. **Total number of aces in the deck:** 4
3. **Total number of fives in the deck:** 4

### Step-by-Step Solution:

1. **Remove the five:**
   - When a five is drawn and removed, we are left with 51 cards in the deck.
   - The remaining deck still has 4 aces.

2. **Probability of drawing an ace as the second card:**
   - Given that there are 51 cards left and 4 of them are aces, the probability of drawing an ace is:

\[ P(\text{ace} | \text{five removed}) = \frac{\text{number of aces left}}{\text{total number of cards left}} = \frac{4}{51} \]

Therefore, the probability \( P(\text{ace} | \text{five}) \) is:

\[ \boxed{\frac{4}{51}} \]

Would you like more details or have any other questions? Here are some related questions you might consider:

1. What is the probability of drawing a king given that a queen was drawn first and removed?
2. What is the probability of drawing a red card given that a black card was drawn first and removed?
3. What is the probability of drawing a face card given that a non-face card was drawn first and removed?
4. What is the probability of drawing a card of the same suit as the removed card?
5. How does the probability change if the first card drawn is not removed but replaced?

### Tip:
When dealing with conditional probabilities, always adjust the total number of possible outcomes based on the given condition.

Learn how to calculate the probability of drawing an ace from a deck after removing a five. This problem involves conditional probability and basic counting principles. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation