Calculating the Odds of an Event
Here you’ll calculate odds by using outcomes or probability. Have you ever thought about the likelihood of an event happening? Take a look at this dilemma:
Guidance
You’ve seen that the probability of an event is defined as a ratio that compares the favorable out comes to the total outcomes. We can write this ratio in fraction form. Sometimes people express the likelihood of events in terms of odds rather than probabilities. The odds of an event occurring are equal to the ratio of favorable outcomes to unfavorable outcomes.
- favorable outcomes = 1(red)
- unfavorable outcomes = 2(blue, yellow)
- total outcomes = 3

Odds in favor of rain: 7 to 3
These odds tell you not only the odds of rain, but also the odds of not raining. If the odds in favor or rain are 7 to 3, then the odds against rain are:Odds against rain: 3 to 7
Another way of saying that is:Odds that it will NOT rain: 3 to 7
You can use this idea in many different situations. If you know the odds that something will happen, then you also know the odds that it will not happen. Use this spinner to calculate odds.
Example A
Odds in favor of spinning a blue. Solution:Example B
Odds in favor of spinning a red or blue. Solution:Example C
Odds against spinning a red or blue. Solution:Intro Problem Revisited
Now let’s go back to the dilemma from the beginning of the reading. Answer all three questions. What are the chances that it won’t rain? We know that the odds of it raining is 4 to 5. Therefore it is a 1 out of 5 chance that it won’t rain. Not very good odds. What are the odds that it will as a percentage? 4 to 5 can be written as a percentage: 80% chance of rain. What are the odds that it won’t as a percentage? 1 to 5 can be written as a percentage: 20% chance that it won’t rain.Guided Practice
Here is one for you to try on your own. What are the odds in favor of a number cube landing on 4?Step 1
Find the favorable and unfavorable outcomes.- favorable outcomes = 1(4)
- unfavorable outcomes = 5(1,2,3,5,6)
Step 2
Write the ratio of favorable to unfavorable outcomes. The odds in favor of rolling a 4 are 1 to 5.Vocabulary
Disjoint events: events that don’t have any outcomes in common. Complementary events: probability that has a sum of 100%. Either/Or events are complementary events.Watch This: Video Review
https://youtu.be/76XEBRaelD0Practice Questions
Solve the problems.- For rolling a number cube, what are the odds in favor of rolling a 2?
- For rolling a number cube, what are the odds against rolling a 2?
- For rolling a number cube, what are the odds in favor of rolling a number greater than 3?
- For rolling a number cube, what are the odds in favor rolling a number less than 5?
- For rolling a number cube, what are the odds against rolling a number less than 5?
- For rolling a number cube, what are the odds in favor of rolling an even number?
- For rolling a number cube, what are the odds against rolling an even number?
- For spinning the spinner, what are the odds in favor of the arrow landing on 10?
- For spinning the spinner, what are the odds in favor of the arrow landing on a 2 or 3?
- For spinning the spinner, what are the odds in favor of the arrow landing on 7, 8 or 9?
- For spinning the spinner, what are the odds in favor of NOT landing on an even number?
- For spinning the spinner, what are the odds of the arrow NOT landing on 10?
- For spinning the spinner, what are the odds in favor of the arrow landing on a number greater than 2?
- For spinning the spinner, what are the odds in favor of the arrow NOT landing on a number greater than 2?
- For spinning the spinner, what are the odds of the arrow not landing on a number greater than 3?