Statistical ratios | Randomness
Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics. Odds also have a simple relation with probability: the odds of an outcome are the ratio of the probability that the outcome occurs to the probability that the outcome does not occur. In mathematical terms, where is the probability of the outcome: where is the probability that the outcome does not occur. Odds can be demonstrated by examining rolling a six-sided die. The odds of rolling a 6 is 1:5. This is because there is 1 event (rolling a 6) that produces the specified outcome of "rolling a 6", and 5 events that do not (rolling a 1,2,3,4 or 5). The odds of rolling either a 5 or 6 is 2:4. This is because there are 2 events (rolling a 5 or 6) that produce the specified outcome of "rolling either a 5 or 6", and 4 events that do not (rolling a 1, 2, 3 or 4). The odds of not rolling a 5 or 6 is the inverse 4:2. This is because there are 4 events that produce the specified outcome of "not rolling a 5 or 6" (rolling a 1, 2, 3 or 4) and two that do not (rolling a 5 or 6). The probability of an event is different, but related, and can be calculated from the odds, and vice versa. The probability of rolling a 5 or 6 is the fraction of the number of events over total events or 2/(2+4), which is 1/3, 0.33 or 33%. When gambling, odds are often the ratio of winnings to the stake and you also get your wager returned. So wagering 1 at 1:5 pays out 6 (5 + 1). If you make 6 wagers of 1, and win once and lose 5 times, you will be paid 6 and finish square. Wagering 1 at 1:1 (Evens) pays out 2 (1 + 1) and wagering 1 at 1:2 pays out 3 (1 + 2). These examples may be displayed in many different forms: * Fractional odds with a slash: 5 (5/1 against), 1/1 (Evens), 1/2 (on) (short priced horse). * Tote boards use decimal or Continental odds (the ratio of total paid out to stake), e.g. 6.0, 2.0, 1.5 * In the US Moneyline a positive number lists winnings per $100 wager; a negative number the amount to wager in order to win $100 on a short-priced horse: 500, 100/–100, –200. (Wikipedia).
This video explains how to determine the probability of an outcome given the odds of an outcome. http://mathispower4u.com
From playlist Probability
This video provides an introductory lesson with several examples for odds. http://mathispower4u.com
From playlist Probability
Ex: Determine Probability Given Odds
This video explains how to determine probability given odds.
From playlist Probability
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From playlist Contests and Sweepstakes odds
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This video explains how to determine odds in favor and odds against a specific die roll. http://mathispower4u.com
From playlist Probability
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From playlist iLecturesOnline: Probability & Stats 2: Random Variable & Probability Distribution
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The odds aren't as odd as you might think, and the log of the odds is even simpler! This StatQuest covers those subjects so that you can understand the statistics for true/false type problems (like Logistic Regression). For a complete index of all the StatQuest videos, check out: https://
From playlist Statistics Fundamentals
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From playlist GEOMETRY CH 2 PROOFS & REASONING
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From playlist Precalculus - College Algebra/Trigonometry
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From playlist Probability
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From playlist New Calculus Video Playlist