Suppose Nate wins 34% of all checker games. (a) What is the probability that Nate wins two checker games in a row? (b) What is the probability that Nate wins six checker games in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Nate wins six checker games in a row, but does not win seven in a row. (a) The probability that Nate wins two checker games in a row is (Round to four decimal places as needed.) (b) The probability that Nate wins six checker games in a row is (Round to four decimal places as needed.) (c) The probability that Nate wins six checker games in a row, but does not win seven in a row is (Round to four decimal places as needed.)
Suppose Nate wins 34% of all checker games. (a) What is the probability that Nate wins two checker games in a row? (b) What is the probability that Nate wins six checker games in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Nate wins six checker games in a row, but does not win seven in a row. (a) The probability that Nate wins two checker games in a row is (Round to four decimal places as needed.) (b) The probability that Nate wins six checker games in a row is (Round to four decimal places as needed.) (c) The probability that Nate wins six checker games in a row, but does not win seven in a row is (Round to four decimal places as needed.)
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.9: Independent And Dependent Events
Problem 3C
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![### Probability Questions on Sequential Wins in Checkers
#### Problem Scenario:
Suppose Nate wins 34% of all checker games.
#### Questions:
(a) What is the probability that Nate wins two checker games in a row?
(b) What is the probability that Nate wins six checker games in a row?
(c) When events are independent, their complements are independent as well. Use this result to determine the probability that Nate wins six checker games in a row, but does not win seven in a row.
---
### Solution:
**(a)** The probability that Nate wins two checker games in a row is:
\[ \boxed{\hspace{2cm}} \]
*(Round to four decimal places as needed.)*
**(b)** The probability that Nate wins six checker games in a row is:
\[ \boxed{\hspace{2cm}} \]
*(Round to four decimal places as needed.)*
**(c)** The probability that Nate wins six checker games in a row, but does not win seven in a row is:
\[ \boxed{\hspace{2cm}} \]
*(Round to four decimal places as needed.)*
#### Explanation:
1. **Probability of Consecutive Wins:**
- The probability of winning a single game is 34% or 0.34.
- The events are independent, so the probability of Nate winning multiple games in a row is the product of the probabilities of each individual game win.
2. **(a) Two Games in a Row:**
- Probability (2 wins) = \((0.34)^2\).
3. **(b) Six Games in a Row:**
- Probability (6 wins) = \((0.34)^6\).
4. **(c) Six Wins Followed by a Loss:**
- First, calculate the probability of six wins, as in (b).
- Then, multiply it by the probability of a loss (which is the complement of the win probability).
- Probability of a loss = \(1 - 0.34 = 0.66\).
- Probability (6 wins followed by a loss) = \((0.34)^6 \times 0.66\).
Please fill in the calculations as necessary and round to four decimal places as indicated.
---
**Graph Explanation:**
There are no graphs present in this problem scenario. The task involves calculations based on](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4175707-d254-4126-a791-753312836f35%2F316a68af-3d46-4045-b00e-22de6f1110ec%2F4d18ges_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Questions on Sequential Wins in Checkers
#### Problem Scenario:
Suppose Nate wins 34% of all checker games.
#### Questions:
(a) What is the probability that Nate wins two checker games in a row?
(b) What is the probability that Nate wins six checker games in a row?
(c) When events are independent, their complements are independent as well. Use this result to determine the probability that Nate wins six checker games in a row, but does not win seven in a row.
---
### Solution:
**(a)** The probability that Nate wins two checker games in a row is:
\[ \boxed{\hspace{2cm}} \]
*(Round to four decimal places as needed.)*
**(b)** The probability that Nate wins six checker games in a row is:
\[ \boxed{\hspace{2cm}} \]
*(Round to four decimal places as needed.)*
**(c)** The probability that Nate wins six checker games in a row, but does not win seven in a row is:
\[ \boxed{\hspace{2cm}} \]
*(Round to four decimal places as needed.)*
#### Explanation:
1. **Probability of Consecutive Wins:**
- The probability of winning a single game is 34% or 0.34.
- The events are independent, so the probability of Nate winning multiple games in a row is the product of the probabilities of each individual game win.
2. **(a) Two Games in a Row:**
- Probability (2 wins) = \((0.34)^2\).
3. **(b) Six Games in a Row:**
- Probability (6 wins) = \((0.34)^6\).
4. **(c) Six Wins Followed by a Loss:**
- First, calculate the probability of six wins, as in (b).
- Then, multiply it by the probability of a loss (which is the complement of the win probability).
- Probability of a loss = \(1 - 0.34 = 0.66\).
- Probability (6 wins followed by a loss) = \((0.34)^6 \times 0.66\).
Please fill in the calculations as necessary and round to four decimal places as indicated.
---
**Graph Explanation:**
There are no graphs present in this problem scenario. The task involves calculations based on
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