https://file.aiquickdraw.com/mathbot/file/1726869597870abtcs7tp.jpg

Let's break down the question from the image:

### Problem Summary:
You have a deck of 5 cards, numbered 1 to 5:
- Cards numbered 3 and 4 are **grey**.
- Cards numbered 1, 2, and 5 are **white**.

A card is drawn at random, and:
- Let \( X \) be the event that the card drawn is **grey**.
- \( P(X) \) represents the probability of drawing a grey card.
- \( \neg X \) (not \( X \)) is the event that the card drawn is **not grey**, i.e., white.
- \( P(\neg X) \) represents the probability of drawing a card that is not grey.

### Part (a):
You need to list the events \( X \) and \( \neg X \), and find their probabilities.

- For \( X \), the outcomes are the grey cards, which are cards numbered 3 and 4. Therefore:
  \[
  X = \{3, 4\}
  \]
  The probability of drawing a grey card is:
  \[
  P(X) = \frac{\text{Number of grey cards}}{\text{Total number of cards}} = \frac{2}{5}
  \]

- For \( \neg X \), the outcomes are the cards that are not grey, which are cards numbered 1, 2, and 5. Therefore:
  \[
  \neg X = \{1, 2, 5\}
  \]
  The probability of drawing a card that is not grey is:
  \[
  P(\neg X) = \frac{3}{5}
  \]

### Part (b):
You need to compute:
\[
1 - P(\neg X)
\]
Substitute the value of \( P(\neg X) \):
\[
1 - P(\neg X) = 1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \frac{2}{5}
\]

### Part (c):
You are asked to compare:
\[
1 - P(\neg X)
\]
with some other probability. From the previous calculation, we found:
\[
1 - P(\neg X) = \frac{2}{5}
\]
But from Part (a), we also know that \( P(X) = \frac{2}{5} \). So:
\[
1 - P(\neg X) = P(X)
\]
Thus, the correct answer is that \( 1 - P(\neg X) \) is the same as \( P(X) \).

### Summary:
- \( P(X) = \frac{2}{5} \)
- \( P(\neg X) = \frac{3}{5} \)
- \( 1 - P(\neg X) = \frac{2}{5} \)
- \( 1 - P(\neg X) \) is the same as \( P(X) \).

Would you like further clarification or additional details?

Here are 5 related questions to expand your understanding:
1. What is the complement rule in probability?
2. How do we calculate probabilities when events are mutually exclusive?
3. What is the significance of the sum of probabilities in a complete sample space?
4. How would the probabilities change if more grey cards were added?
5. Can you explain the difference between independent and mutually exclusive events?

**Tip**: Always verify that the total probabilities in a sample space add up to 1 for validation.

We have a deck of 5 cards numbered from 1 to 5. Some are grey and some are white. The cards numbered 3 and 4 are grey. The cards numbered 1, 2, and 5 are white. A card is drawn at random. Let X be the event that the card is grey, and let P(X) be the probability of X. Let not X be the event that the card is not grey, and let P(not X) be the probability of not X. The task is to find the probability of these events and perform additional calculations related to the probabilities.

Learn how to calculate the probability of drawing a grey or white card from a deck of 5 cards. This problem covers key probability concepts such as complementary events and the complement rule in probability. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation