Textbook Question
23. Footrace There are 72 runners in a 10-kilometer race. How many ways can the runners finish first, second, and third?
Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.1.92
Odds The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read "2 to 3"). In Exercises 91-96, use this information about odds.
92. The probability of winning an instant prize game is 1/10. The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning.
Verified step by step guidance1
Step 1: Understand the relationship between probability and odds. Probability is the ratio of successful outcomes to the total number of outcomes, while odds are the ratio of successful outcomes to unsuccessful outcomes. For example, if the probability of winning is P, then the odds of winning are P : (1 - P).
Step 2: For the first game, the probability of winning is given as 1/10. Calculate the odds of winning for this game using the formula: Odds = P : (1 - P). Substitute P = 1/10 into the formula to find the odds.
Step 3: For the second game, the odds of winning are given as 1 : 10. To compare this with the first game, convert these odds into probability using the formula: Probability = Successful Outcomes / (Successful Outcomes + Unsuccessful Outcomes). Substitute the values from the odds (1 and 10) into the formula to calculate the probability.
Step 4: Compare the probabilities of winning for both games. The game with the higher probability of winning offers the better chance of success.
Step 5: Based on the comparison, determine which game you should play and explain your reasoning by referencing the calculated probabilities and their relationship to the given odds.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Odds vs. Probability
Odds and probability are two ways to express the likelihood of an event occurring. Probability is the ratio of successful outcomes to the total number of outcomes, while odds compare successful outcomes to unsuccessful ones. For example, if the probability of winning is 1/10, the odds of winning are 1:9, since there is one successful outcome and nine unsuccessful ones.
Recommended video:
Guided course
04:39
Visualizing Qualitative vs. Quantitative Data
Calculating Odds
Calculating odds involves determining the ratio of successful outcomes to unsuccessful outcomes. If a game has a probability of winning of 1/10, it means there is one winning outcome for every nine losing outcomes, resulting in odds of 1:9. Understanding how to convert between probability and odds is essential for making informed decisions about which game to play.
Recommended video:
Guided course
03:26Calculating the Median
Comparing Odds
When comparing odds from different games, it is crucial to determine which game offers a better chance of winning. In the given scenario, one game has odds of 1:10, while the other has a probability of 1/10 (or odds of 1:9). By comparing these values, players can choose the game that maximizes their chances of winning.
Recommended video:
Guided course
04:48Comparing Mean vs. Median
Related Practice
Textbook Question
"Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.
36. You randomly select one card from a standard deck of 52 playing cards. Event B is selecting the ace of spades."
Textbook Question
3. What does the notation P(B|A) mean?
Textbook Question
Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.
46. Event F: rolling a number divisible by 5
Textbook Question
True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false,
explain why.
4. When two events are independent, they are also mutually exclusive.
Textbook Question
Graphical Analysis In Exercises 7 and 8, determine whether the events shown in the Venn diagram are mutually exclusive. Explain your reasoning.