Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN: 9780547587776
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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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](https://content.bartleby.com/qna-images/question/f4175707-d254-4126-a791-753312836f35/316a68af-3d46-4045-b00e-22de6f1110ec/4d18ges_processed.png)
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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- In Example 8, what is the probability that an employee chosen at random has 30 or more years of service?arrow_forwardYou toss two six-sided dice. What is the probability that the total of the two dice is 5?arrow_forwardDividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an 8,000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning and that of B winning if the game were to continue? The French Mathematician Pascal and Fermat corresponded about this problem, and both came to the same correct calculations though by very different reasonings. Their friend Roberval disagreed with both of them. He argued that player A has probability 34 of winning, because the game can end in the four ways H, TH, TTH, TTT and in three of these, A wins. Robervals reasoning was wrong. a Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform the experiment 80 or more times, and estimate the probability that player A wins. bCalculate the probability that player A wins. Compare with your estimate from part a.arrow_forward
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