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\r\n\r\nThink about the odds for the arrow of the spinner above landing on red:\r\n- \r\n \t
- favorable outcomes = 1(red)<\/li>\r\n \t
- unfavorable outcomes = 2(blue, yellow)<\/li>\r\n \t
- total outcomes = 3<\/li>\r\n<\/ul>\r\nSo the probability<\/em> of spinning red is:\r\n\r\n[latex]P(\\text{red})=\\frac{\\text{favorable outcomes}}{\\text{total outcomes}}=\\frac{1}{3}\\\\[\/latex]\r\n\r\nWhile the odds<\/em> in favor of red are:\r\n\r\n[latex]\\text{Odds(in favor of red)}=\\frac{\\text{favorable outcomes}}{\\text{unfavorable outcomes}}=\\frac{1}{2}\\\\[\/latex]\r\n\r\nOdds against an event occurring are defined as:\r\n\r\n[latex]\\text{Odds(against red)}=\\frac{\\text{unfavorable outcomes}}{\\text{favorable outcomes}}=\\frac{2}{1}\\\\[\/latex]\r\n\r\nYou can solve any probability problem in terms of odds rather than probabilities. Notice that the ratio\u00a0represents what is being compared. Be sure that your numbers match the comparison.<\/strong>\r\n\r\nWe can use odds to calculate how likely an event is to happen. We can compare the odds in favor of an event with\u00a0the probability that the event will actually occur. Let\u2019s look at an example.\r\n\r\nTake a look at this situation.\r\n\r\nYou\u2019ve seen that the odds in favor of an event (E<\/em>) occurring are shown in this ratio.\r\n\r\n[latex]\\text{Odds(in favor of)}E=\\frac{\\text{favorable outcomes}}{\\text{unfavorable outcomes}}=\\frac{1}{2}\\\\[\/latex]\r\n\r\nAnd the odds against the same event occurring are:\r\n\r\n[latex]\\text{Odds(against)}E=\\frac{\\text{unfavorable outcomes}}{\\text{favorable outcomes}}=\\frac{2}{1}\\\\[\/latex]\r\n\r\nYou can use these two facts to compute the ratio of things happening and not happening.<\/strong>\r\n\r\n
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For example, suppose the weather forecast states:\r\nOdds in favor of rain: 7 to 3<\/p>\r\nThese odds tell you not only the odds of rain, but also the odds of not raining.\r\n\r\nIf the odds in favor or rain are 7 to 3, then the odds against rain are:\r\n
Odds against rain: 3 to 7<\/p>\r\nAnother way of saying that is:\r\n
Odds that it will NOT rain: 3 to 7<\/p>\r\nYou can use this idea in many different situations. If you know the odds that something will happen, then you\u00a0also know the odds that it will not happen.\r\n\r\nUse this spinner to calculate odds.\r\n\r\n
\r\nExample A<\/h4>\r\nOdds in favor of spinning a blue.\r\n\r\nSolution: [latex]\\frac{1}{2}\\\\[\/latex]\r\n
Example B<\/h4>\r\nOdds in favor of spinning a red or blue.\r\n\r\nSolution: [latex]\\frac{2}{1}\\\\[\/latex]\r\n
Example C<\/h4>\r\nOdds against spinning a red or blue.\r\n\r\nSolution: [latex]\\frac{1}{2}\\\\[\/latex]\r\n
Intro Problem Revisited<\/h2>\r\nNow let\u2019s go back to the dilemma from the beginning of the reading.\r\n\r\nAnswer all three questions.\r\n\r\nWhat are the chances that it won\u2019t rain?\u00a0<\/strong>We know that the odds of it raining is 4 to 5. Therefore it is a 1 out of 5 chance that it won\u2019t rain. Not very\u00a0good odds.\r\n\r\nWhat are the odds that it will as a percentage?\u00a0<\/strong>4 to 5 can be written as a percentage: 80% chance of rain.\r\n\r\nWhat are the odds that it won\u2019t as a percentage?\u00a0<\/strong>1 to 5 can be written as a percentage: 20% chance that it won\u2019t rain.\r\n
\r\nGuided Practice<\/h3>\r\nHere is one for you to try on your own.\r\n\r\nWhat are the odds in favor of a regular six sided dice landing on 4?\r\n
Step 1<\/h4>\r\nFind the favorable and unfavorable outcomes.\r\n
- \r\n \t
- favorable outcomes = 1(4)<\/li>\r\n \t
- unfavorable outcomes = 5(1,2,3,5,6)<\/li>\r\n<\/ul>\r\n
Step 2<\/h4>\r\nWrite the ratio of favorable to unfavorable outcomes.\r\n\r\n[latex]\\text{Odds}(4) = \\frac{\\text{favorable outcomes}}{\\text{unfavorable outcomes}}=\\frac{1}{5}\\\\[\/latex]\r\n\r\nThe odds in favor of rolling a 4 are 1 to 5.\r\n\r\n<\/div>","rendered":"
Here you\u2019ll calculate odds by using outcomes or probability.\u00a0Have you ever thought about the likelihood of an event happening? Take a look at this dilemma:<\/p>\n
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Telly and Carey were already hard at work when Ms. Kelley came into the bike shop on Thursday morning. It was\u00a0three days before the big race and there was still a lot of work to be done.<\/p>\n\u201cI can\u2019t believe it!\u201d Ms. Kelley exclaimed as she came into the shop.<\/p>\n
\u201cWhat?\u201d both girl asked alarmed.<\/p>\n
\u201cThere is a 4 to 5 chance that it is going to rain on Saturday. I just heard the weather report,\u201d Ms. Kelley said sighing.<\/p>\n
\u201cWell, there is still a chance that it won\u2019t,\u201d Telly said trying to cheer her up.<\/p>\n
When we think about chances and odds, we can calculate the likelihood that an event will or won\u2019t occur. In\u00a0this case, there are odds that it will rain and odds that it won\u2019t. We can also express those odds as a fraction\u00a0or a percentage. Learn about odds in this reading,\u00a0and you can work on the odds of the rainstorm at the end.<\/p>\n
Guidance<\/h2>\n
You\u2019ve seen that the probability of an event is defined as a ratio that compares the favorable out comes to the total\u00a0outcomes. We can write this ratio in fraction form.<\/p>\n
[latex]P(\\text{event})=\\frac{\\text{favorable outcomes}}{\\text{total outcomes}}\\\\[\/latex]<\/p>\n
Sometimes people express the likelihood of events in terms of odds<\/strong> rather than probabilities. The odds of an event\u00a0occurring are equal to the ratio of favorable outcomes to unfavorable outcomes<\/strong>.<\/p>\n
<\/p>\nThink about the odds for the arrow of the spinner above landing on red:<\/p>\n
- \n
- favorable outcomes = 1(red)<\/li>\n
- unfavorable outcomes = 2(blue, yellow)<\/li>\n
- total outcomes = 3<\/li>\n<\/ul>\n
So the probability<\/em> of spinning red is:<\/p>\n
[latex]P(\\text{red})=\\frac{\\text{favorable outcomes}}{\\text{total outcomes}}=\\frac{1}{3}\\\\[\/latex]<\/p>\n
While the odds<\/em> in favor of red are:<\/p>\n
[latex]\\text{Odds(in favor of red)}=\\frac{\\text{favorable outcomes}}{\\text{unfavorable outcomes}}=\\frac{1}{2}\\\\[\/latex]<\/p>\n
Odds against an event occurring are defined as:<\/p>\n
[latex]\\text{Odds(against red)}=\\frac{\\text{unfavorable outcomes}}{\\text{favorable outcomes}}=\\frac{2}{1}\\\\[\/latex]<\/p>\n
You can solve any probability problem in terms of odds rather than probabilities. Notice that the ratio\u00a0represents what is being compared. Be sure that your numbers match the comparison.<\/strong><\/p>\n
We can use odds to calculate how likely an event is to happen. We can compare the odds in favor of an event with\u00a0the probability that the event will actually occur. Let\u2019s look at an example.<\/p>\n
Take a look at this situation.<\/p>\n
You\u2019ve seen that the odds in favor of an event (E<\/em>) occurring are shown in this ratio.<\/p>\n
[latex]\\text{Odds(in favor of)}E=\\frac{\\text{favorable outcomes}}{\\text{unfavorable outcomes}}=\\frac{1}{2}\\\\[\/latex]<\/p>\n
And the odds against the same event occurring are:<\/p>\n
[latex]\\text{Odds(against)}E=\\frac{\\text{unfavorable outcomes}}{\\text{favorable outcomes}}=\\frac{2}{1}\\\\[\/latex]<\/p>\n
You can use these two facts to compute the ratio of things happening and not happening.<\/strong><\/p>\n
For example, suppose the weather forecast states:<\/p>\nOdds in favor of rain: 7 to 3<\/p>\n
These odds tell you not only the odds of rain, but also the odds of not raining.<\/p>\n
If the odds in favor or rain are 7 to 3, then the odds against rain are:<\/p>\n
Odds against rain: 3 to 7<\/p>\n
Another way of saying that is:<\/p>\n
Odds that it will NOT rain: 3 to 7<\/p>\n
You can use this idea in many different situations. If you know the odds that something will happen, then you\u00a0also know the odds that it will not happen.<\/p>\n
Use this spinner to calculate odds.<\/p>\n
<\/p>\nExample A<\/h4>\n
Odds in favor of spinning a blue.<\/p>\n
Solution: [latex]\\frac{1}{2}\\\\[\/latex]<\/p>\n
Example B<\/h4>\n
Odds in favor of spinning a red or blue.<\/p>\n
Solution: [latex]\\frac{2}{1}\\\\[\/latex]<\/p>\n
Example C<\/h4>\n
Odds against spinning a red or blue.<\/p>\n
Solution: [latex]\\frac{1}{2}\\\\[\/latex]<\/p>\n
Intro Problem Revisited<\/h2>\n
Now let\u2019s go back to the dilemma from the beginning of the reading.<\/p>\n
Answer all three questions.<\/p>\n
What are the chances that it won\u2019t rain?\u00a0<\/strong>We know that the odds of it raining is 4 to 5. Therefore it is a 1 out of 5 chance that it won\u2019t rain. Not very\u00a0good odds.<\/p>\n
What are the odds that it will as a percentage?\u00a0<\/strong>4 to 5 can be written as a percentage: 80% chance of rain.<\/p>\n
What are the odds that it won\u2019t as a percentage?\u00a0<\/strong>1 to 5 can be written as a percentage: 20% chance that it won\u2019t rain.<\/p>\n
\nGuided Practice<\/h3>\n
Here is one for you to try on your own.<\/p>\n
What are the odds in favor of a regular six sided dice landing on 4?<\/p>\n
Step 1<\/h4>\n
Find the favorable and unfavorable outcomes.<\/p>\n
- \n
- favorable outcomes = 1(4)<\/li>\n
- unfavorable outcomes = 5(1,2,3,5,6)<\/li>\n<\/ul>\n
Step 2<\/h4>\n
Write the ratio of favorable to unfavorable outcomes.<\/p>\n
[latex]\\text{Odds}(4) = \\frac{\\text{favorable outcomes}}{\\text{unfavorable outcomes}}=\\frac{1}{5}\\\\[\/latex]<\/p>\n
The odds in favor of rolling a 4 are 1 to 5.<\/p>\n<\/div>\n\n\t\t\t
\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tCC licensed content, Shared previously<\/div>- Calculate Odds using Outcomes or Probability. Authored by<\/strong>: Jen Kershaw. Provided by<\/strong>: CK-12 Foundation. Located at<\/strong>: http:\/\/www.ck12.org\/<\/a>. License<\/strong>: CC BY-NC: Attribution-NonCommercial<\/a><\/em><\/li><\/ul>