This exercise assumes familiarity with counting arguments and probability (see Probability and Counting Techniques). Kent's Tents has eight green knapsacks and four yellow ones in stock. Curt selects four of them at random. Let X be the number of green knapsacks he selects. Give the probability distribution. (Enter your probabilities as fractions.) X 0 1 2 3 4 P(X = x) X X X X Find P(X ≤ 2). (Enter your probability as a fraction.) P(X ≤ 2) =
This exercise assumes familiarity with counting arguments and probability (see Probability and Counting Techniques). Kent's Tents has eight green knapsacks and four yellow ones in stock. Curt selects four of them at random. Let X be the number of green knapsacks he selects. Give the probability distribution. (Enter your probabilities as fractions.) X 0 1 2 3 4 P(X = x) X X X X Find P(X ≤ 2). (Enter your probability as a fraction.) P(X ≤ 2) =
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This exercise assumes familiarity with counting arguments and probability (see Probability and Counting Techniques).
Kent's Tents has eight green knapsacks and four yellow ones in stock. Curt selects four of them at random. Let X be the number of green knapsacks he selects. Give the probability distribution. (Enter your probabilities as fractions.)
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| P(X = x) |
Find
P(X ≤ 2).
(Enter your probability as a fraction.)P(X≤ 2) =
PLEASE USE FRACTIONS! :)
![### Probability Distribution and Counting Arguments
#### Introduction
This exercise assumes familiarity with counting arguments and probability (see Probability and Counting Techniques).
#### Problem Statement
Kent's Tents has eight green knapsacks and four yellow ones in stock. Curt selects four of them at random. Let \(X\) be the number of green knapsacks he selects. Give the probability distribution. (Enter your probabilities as fractions.)
#### Probability Distribution Table
| \(x\) | 0 | 1 | 2 | 3 | 4 |
|------|---|---|---|---|---|
| \(P(X = x)\) | | | | | |
Each cell that has a red "×" indicates an incorrect response.
#### Question
Find \( P(X \leq 2) \). (Enter your probability as a fraction.)
\[ P(X \leq 2) = \]
#### Explanation on Graph
The table provided is meant to help in visualizing and calculating the probabilities. Fill in the table with fractions representing the probabilities \( P(X = x) \) for \( x \) ranging from 0 to 4, based on the selection of the green knapsacks. Make sure to use counting techniques to derive these probabilities accurately.
### Steps to Solve
1. Calculate the total number of ways to choose 4 knapsacks out of 12 (using combinations).
2. Determine the number of favorable outcomes for each possible value of \(X\) (from 0 to 4 green knapsacks).
3. Divide the number of favorable outcomes by the total number of outcomes to get the probabilities \( P(X = x) \).
4. Add up the probabilities for \( X = 0, 1, 2 \) to find \( P(X \leq 2) \).
Note: Ensure your final answer is entered as a fraction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62f7585f-4634-4199-81a6-58188b278fc8%2F8175ff66-79fb-48fd-bd1f-397eaf3c7c52%2Fll9o6_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Distribution and Counting Arguments
#### Introduction
This exercise assumes familiarity with counting arguments and probability (see Probability and Counting Techniques).
#### Problem Statement
Kent's Tents has eight green knapsacks and four yellow ones in stock. Curt selects four of them at random. Let \(X\) be the number of green knapsacks he selects. Give the probability distribution. (Enter your probabilities as fractions.)
#### Probability Distribution Table
| \(x\) | 0 | 1 | 2 | 3 | 4 |
|------|---|---|---|---|---|
| \(P(X = x)\) | | | | | |
Each cell that has a red "×" indicates an incorrect response.
#### Question
Find \( P(X \leq 2) \). (Enter your probability as a fraction.)
\[ P(X \leq 2) = \]
#### Explanation on Graph
The table provided is meant to help in visualizing and calculating the probabilities. Fill in the table with fractions representing the probabilities \( P(X = x) \) for \( x \) ranging from 0 to 4, based on the selection of the green knapsacks. Make sure to use counting techniques to derive these probabilities accurately.
### Steps to Solve
1. Calculate the total number of ways to choose 4 knapsacks out of 12 (using combinations).
2. Determine the number of favorable outcomes for each possible value of \(X\) (from 0 to 4 green knapsacks).
3. Divide the number of favorable outcomes by the total number of outcomes to get the probabilities \( P(X = x) \).
4. Add up the probabilities for \( X = 0, 1, 2 \) to find \( P(X \leq 2) \).
Note: Ensure your final answer is entered as a fraction.
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