### 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

Name: ### Probability Questions on Sequential Wins in Checkers#### Problem
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Description: ### 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

Probability is a concept that everyone uses in their day-to-day life. We use the word probably, for…

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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.)

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.FOM: Focus On Modeling: The Monte Carlo Method

Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...

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