Odds Chance
Probability tells us how often some event will happen after many repeated trials. This topic covers theoretical, experimental, compound probability, permutations, combinations, and more! Our mission is to provide a free, world-class education to anyone, anywhere. Summary: The probability of an event is the measure of the chance that the event will occur as a result of an experiment. The probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes. A 1 in 500 chance of winning, or probability of winning, is entered into this calculator as '1 to 500 Odds are for winning'. You may also see odds reported simply as chance of winning as 500:1. This most likely means '500 to 1 Odds are against winning' which is.
You might have noticed that we make statements like the trains may be late, it may take an hour, to reach home and so forth. This type of statements indicates the probability of an event, as its occurrence is not certain. It implies the extent to which an event is possible to happen.
Probability is divided into two types, objective and subjective probability. Subjective probability is based on attitude, belief, knowledge, judgment and experience of the person. In mathematics, we study objective probability.
Probability is not similar to odds, as it represents the probability that the event will happen, upon the probability that the event will not happen. Now, let’s take a look at the difference between odds and probability provided in the article below.
Content: Odds Vs Probability
Comparison Chart
| Basis for Comparison | Odds | Probability |
|---|---|---|
| Meaning | Odds refers to the chances in favor of the event to the chances against it. | Probability refers to the likelihood of occurrence of an event. |
| Expressed in | Ratio | Percent or decimal |
| Lies between | 0 to ∞ | 0 to 1 |
| Formula | Occurrence/Non-occurrence | Occurrence/Whole |
Definition of Odds
In mathematics, the term odds can be defined as the ratio of number of favourable events to the number of unfavourable events. While odds for an event indicates the probability that the event will occur, whereas odds against will reflect the likelihood of non-occurrence of the event. In finer terms, odds is described as the probability that a certain event will happen or not.
Odds can range from zero to infinity, wherein if the odds is 0, the event is not likely to happen, but if it is ∞, then it is more likely to happen.
For example Suppose, there are 20 marbles in a bag, eight are red, six are blue, and six are yellow. If one marble is to be picked at random, then the odds of getting red marble is 8/12 or say 2:3
Definition of Probability
Probability is a mathematical concept, which is concerned with likelihood the occurrence of a particular event. It forms the basis for a theory for testing of hypothesis and theory of estimation. It can be expressed as the ratio of the number of events favourable to a specific event, to the total number of events.
Probability ranges from 0 and 1, both inclusive. So, when the probability of an event is 0, it denotes an impossible event, whereas when it is 1, it is an indicator of the certain or sure event. In short, the higher the probability of an event, the greater are the chances of the occurrence of the event.
For example: Suppose a dartboard is divided into 12 parts, for 12 zodiacs. Now, if a dart is targeted, the chances of occurrence of areas are 1/12, as the favourable event is 1, i.e. Aries and a total number of events are 12, that can be denoted as 0.08 or 8%.
Key Differences Between Odds and Probability
The differences between odds and probability are discussed in the points given below:
- The term ‘odds’ is used to describe that if there are any chances of the occurrence of an event or not. As against, probability determines, the likelihood of the happening of an event, i.e. how often the event will take place.
- While odds are expressed in the ratio, the probability is either written in percentage form or decimal.
- Odds usually ranges from zero to infinity, wherein zero defines impossibility of occurrence of an event, and infinity denotes the possibility of occurrence. Conversely, probability lies between zero to one. So, the closer the probability to zero, the more are the chances of its non-occurrence and the closer it is to one, the higher are the chances of its occurrence.
- Odds are the ratio of favourable events to the unfavourable event. In contrast, the probability can be calculated by dividing the favourable event by the total number of events.
Conclusion
Probability is a branch of mathematics, which includes odds. One can measure chance, with the help of odds or probability. While odds are a ratio of occurrence to non-occurrence, the probability is the ratio of occurrence to the whole.
Odds Chances Difference
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Odds Chance Synonym
, that is P(B).If events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by
P(A and B) = P(A)P(B A).
From this definition, the conditional probability P(B A) is easily obtained by dividing by P(A):
Note: This expression is only valid when P(A) is greater than 0.
Examples
In a card game, suppose a player needs to draw two cards of the same suit in order to win. Of the 52 cards, there are 13 cards in each suit. Suppose first the player draws a heart. Now the player wishes to draw a second heart. Since one heart has already been chosen, there are now 12 hearts remaining in a deck of 51 cards. So the conditional probability P(Draw second heart First card a heart) = 12/51. Suppose an individual applying to a college determines that he has an 80% chance of being accepted, and he knows that dormitory housing will only be provided for 60% of all of the accepted students. The chance of the student being accepted and receiving dormitory housing is defined by
P(Accepted and Dormitory Housing) = P(Dormitory Housing Accepted)P(Accepted) = (0.60)*(0.80) = 0.48.
Consider the college applicant who has determined that he has 0.80 probability of acceptance and that only 60% of the accepted students will receive dormitory housing. Of the accepted students who receive dormitory housing, 80% will have at least one roommate. The probability of being accepted and receiving dormitory housing and having no roommates is calculated by:
P(Accepted and Dormitory Housing and No Roommates) = P(Accepted)P(Dormitory Housing Accepted)P(No Roomates Dormitory Housing and Accepted) = (0.80)*(0.60)*(0.20) = 0.096. The student has about a 10% chance of receiving a single room at the college.
, which simply states that the probability of event B is the sum of the conditional probabilities of event B given that event A has or has not occurred. For independent events A and B, this is equal to P(B)P(A) + P(B)P(Ac) = P(B)(P(A) + P(Ac)) = P(B)(1) = P(B), since the probability of an event and its complement must always sum to 1. Bayes's formula is defined as follows: Example
Suppose a voter poll is taken in three states. In state A, 50% of voters support the liberal candidate, in state B, 60% of the voters support the liberal candidate, and in state C, 35% of the voters support the liberal candidate. Of the total population of the three states, 40% live in state A, 25% live in state B, and 35% live in state C. Given that a voter supports the liberal candidate, what is the probability that she lives in state B? By Bayes's formula,
The probability that the voter lives in state B is approximately 0.32.