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ODDS

Odds

Definition Of Odds

Odds is the ratio that compares the number of favorable outcomes of an event to the number of unfavorable outcomes.

More About Odds

Odds in Favor: Odds in favor of an event = number of favorable outcomes : number of unfavorable outcomes. 
For example, the odds in favor of rolling a 2 on a fair six-sided die are 1 : 5 or 1 / 5.

Odds against: Odds against an event = number of unfavorable outcomes : number of favorable outcomes.
For example, the odds against rolling a 2 on a fair six-sided die are 5 : 1 or 5/ 1

Video Examples: Odd and Even Numbers

Solved Example on Odds

Ques: Find the odds in favor of getting exactly 1 head when three coins are tossed.

Choices:

A. 3 : 5
B. 5 : 3
C. 2 : 1
D. 1 : 2
Correct answer: A

Solution:

Step 1: Sample space, S = {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}.
Step 2: The odds in favor of getting exactly 1 head are 3 : 5. [Three outcomes are successes and 5 are failures.]

Quick Summary

  • Odds in favor compare favorable outcomes to unfavorable outcomes.
  • Odds against compare unfavorable outcomes to favorable outcomes.
  • Odds are different from probability; probability is favorable outcomes divided by total outcomes.
\[ Odds\ in\ favor = \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}} \]

⚠️ Common Mistakes

  • Confusing odds with probability.
  • Reversing the ratio of favorable to unfavorable outcomes.

🌍 Real-World Uses

  • Gambling: Calculating the odds of winning a lottery or a horse race to determine potential payouts.
  • Insurance: Assessing the odds of an event occurring (e.g., a car accident) to set insurance premiums.
  • Sports analytics: Determining the odds of a team winning a game based on their past performance and other factors.

📋 Standards Alignment

  • CCSS.MATH.SP.7.C.6
  • CCSS.MATH.SP.7.C.7
  • CCSS.MATH.SP.7.C.8

🔗 Related Links

🍎 Teacher Insights

Use real-world examples, like sports betting or games of chance, to illustrate the concept of odds. Emphasize the difference between odds and probability with clear examples.

🎓 Prerequisites

  • Ratios
  • Probability Basics
  • Fractions

Check Your Knowledge

Q1: What are the odds in favor of rolling a 4 on a six-sided die?

Q2: What are the odds against rolling a 4 on a six-sided die?

Q3: If the odds in favor of an event are 2:3, what is the probability of the event occurring?

Frequently Asked Questions

Q: What is the difference between odds and probability?
A: Probability is the ratio of favorable outcomes to the total number of outcomes, while odds is the ratio of favorable outcomes to unfavorable outcomes.

Q: How do I calculate odds in favor?
A: Divide the number of favorable outcomes by the number of unfavorable outcomes.

Q: How do I calculate odds against?
A: Divide the number of unfavorable outcomes by the number of favorable outcomes.

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