Given That the Odds Again an Event E Are 5:24
Hither you'll calculate odds by using outcomes or probability. Accept you ever thought virtually the likelihood of an event happening? Accept a look at this dilemma:
Telly and Carey were already difficult at work when Ms. Kelley came into the bike shop on Thursday morning. It was three days earlier the large race and there was notwithstanding a lot of piece of work to be washed.
"I tin't believe it!" Ms. Kelley exclaimed as she came into the shop.
"What?" both daughter asked alarmed.
"There is a four to 5 chance that information technology is going to rain on Sat. I merely heard the conditions written report," Ms. Kelley said sighing.
"Well, there is nonetheless a chance that it won't," Telly said trying to cheer her up.
When we think about chances and odds, we can calculate the likelihood that an event will or won't occur. In this instance, there are odds that it volition rain and odds that it won't. We can also express those odds equally a fraction or a percentage. Larn about odds in this reading, and you tin can piece of work on the odds of the rainstorm at the end.
Guidance
You've seen that the probability of an outcome is defined as a ratio that compares the favorable out comes to the full outcomes. We tin can write this ratio in fraction course.
[latex]P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}\\[/latex]
Sometimes people express the likelihood of events in terms of odds rather than probabilities. The odds of an result occurring are equal to the ratio of favorable outcomes to unfavorable outcomes.
Recollect about the odds for the arrow of the spinner above landing on red:
- favorable outcomes = one(red)
- unfavorable outcomes = 2(blueish, xanthous)
- total outcomes = 3
So the probability of spinning ruby is:
[latex]P(\text{ruby-red})=\frac{\text{favorable outcomes}}{\text{total outcomes}}=\frac{one}{3}\\[/latex]
While the odds in favor of red are:
[latex]\text{Odds(in favor of red)}=\frac{\text{favorable outcomes}}{\text{unfavorable outcomes}}=\frac{i}{2}\\[/latex]
Odds confronting an event occurring are defined every bit:
[latex]\text{Odds(confronting ruddy)}=\frac{\text{unfavorable outcomes}}{\text{favorable outcomes}}=\frac{2}{one}\\[/latex]
You can solve any probability problem in terms of odds rather than probabilities. Notice that the ratio represents what is existence compared. Be sure that your numbers match the comparison.
Nosotros can use odds to calculate how likely an upshot is to happen. We can compare the odds in favor of an effect with the probability that the effect will actually occur. Let's look at an case.
Have a look at this situation.
You lot've seen that the odds in favor of an outcome (E) occurring are shown in this ratio.
[latex]\text{Odds(in favor of)}Eastward=\frac{\text{favorable outcomes}}{\text{unfavorable outcomes}}=\frac{1}{2}\\[/latex]
And the odds confronting the same consequence occurring are:
[latex]\text{Odds(confronting)}E=\frac{\text{unfavorable outcomes}}{\text{favorable outcomes}}=\frac{ii}{one}\\[/latex]
Y'all tin can use these two facts to compute the ratio of things happening and not happening.
For example, suppose the weather forecast states:
Odds in favor of rain: 7 to iii
These odds tell you not but the odds of rain, simply too the odds of non raining.
If the odds in favor or rain are 7 to 3, so the odds against pelting are:
Odds against rain: 3 to 7
Another mode of saying that is:
Odds that information technology will NOT pelting: 3 to seven
You can use this idea in many different situations. If you know the odds that something will happen, and then you as well know the odds that it will not happen.
Apply this spinner to calculate odds.
Example A
Odds in favor of spinning a blueish.
Solution: [latex]\frac{i}{2}\\[/latex]
Case B
Odds in favor of spinning a crimson or blue.
Solution: [latex]\frac{two}{1}\\[/latex]
Example C
Odds against spinning a red or blue.
Solution: [latex]\frac{one}{2}\\[/latex]
Intro Problem Revisited
Now let's go back to the dilemma from the kickoff of the reading.
Answer all three questions.
What are the chances that it won't rain?We know that the odds of information technology raining is 4 to 5. Therefore it is a one out of v adventure that it won't rain. Non very good odds.
What are the odds that it will as a percent?4 to v tin can be written every bit a percent: eighty% chance of pelting.
What are the odds that it won't as a percentage?1 to v can be written as a percentage: 20% take a chance that it won't rain.
Guided Practise
Here is ane for you to attempt on your own.
What are the odds in favor of a number cube landing on 4?
Step ane
Discover the favorable and unfavorable outcomes.
- favorable outcomes = 1(4)
- unfavorable outcomes = five(1,ii,3,v,6)
Step 2
Write the ratio of favorable to unfavorable outcomes.
[latex]\text{Odds}(4) = \frac{\text{favorable outcomes}}{\text{unfavorable outcomes}}=\frac{1}{5}\\[/latex]
The odds in favor of rolling a 4 are i to v.
Vocabulary
Disjoint events: events that don't have whatsoever outcomes in common.
Complementary events: probability that has a sum of 100%. Either/Or events are complementary events.
Watch This: Video Review
Practice Questions
Solve the problems.
- For rolling a number cube, what are the odds in favor of rolling a two?
- 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 three?
- For rolling a number cube, what are the odds in favor rolling a number less than five?
- For rolling a number cube, what are the odds against rolling a number less than five?
- 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 a spinner numbered i –x, answer the following questions.
- 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 pointer landing on 7, viii or 9?
- For spinning the spinner, what are the odds in favor of Non 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 pointer landing on a number greater than two?
- For spinning the spinner, what are the odds in favor of the arrow NOT landing on a number greater than two?
- For spinning the spinner, what are the odds of the arrow not landing on a number greater than 3?
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Source: https://courses.lumenlearning.com/math4libarts/chapter/calculating-the-odds-of-an-event/
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