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| Basic Definitions |
Basic Definitions
An ‘outcome’ is the specific event that occurs as the result of a process with an aspect of randomness. When tossing a coin, the possible outcomes are a HEAD or a TAIL. When rolling a die, the possible outcomes are 1, 2, 3, 4, 5, or 6. If there is no random aspect involved, then there is no need to use probability.
The term ‘random’ is used here to imply that all of the possible outcomes are equally likely. There is no bias or external influence that would compel one outcome to occur more often than another. In a random process there is no way to predict a specific outcome for just one trial.
If you cannot predict an outcome, what is the point of probability? While you cannot predict the outcome for a single trial, you can predict the pattern of outcomes for a large number of trials, and you can predict the chance of obtaining a particular outcome for a single trial. For example, suppose that a box contains three red balls and seven green balls. If you were blindfolded and selected just one ball – what colour would it be? You cannot guarantee the colour of the selected ball, but the chances are that seven times out of ten the ball would be green.
The ‘probability’ of an event occurring is just the ratio of the number of ways that event can occur, to the total number of possible outcomes. The probability of tossing a coin and getting a HEAD is 1 out of 2, or 0.5. The probability of drawing a HEART from a deck of shuffled bridge cards is 13 out of 52, which reduces to 1 out of 4, or 0.25.
Defined this way, the probability of an event is always a number between zero and one. A probability of zero for an event means that the event will never occur. A probability of 0.33 means the event will occur about one third of the time. A probability of 1.0 means the event will occur every time. Probabilities can be expressed either as fractions or as decimal numbers. The decimal format is usually easier to deal with when several calculations are involved, or a number of probabilities are to be compared.
The ‘odds’ of an event occurring is just the ratio of the number of ways the event can occur, to the number of other possible outcomes. In the example with the three red balls and the seven green balls, the probability of selecting a red ball is 3 out of 10 or 0.3, while the odds of selecting a red ball are 3 to 7. The odds notation is often used when making wagers.
The probability and odds notations emphasize different aspects of the same information. The probability notation has a greater range of application.
An ‘outcome’ is the specific event that occurs as the result of a process with an aspect of randomness. When tossing a coin, the possible outcomes are a HEAD or a TAIL. When rolling a die, the possible outcomes are 1, 2, 3, 4, 5, or 6. If there is no random aspect involved, then there is no need to use probability.
The term ‘random’ is used here to imply that all of the possible outcomes are equally likely. There is no bias or external influence that would compel one outcome to occur more often than another. In a random process there is no way to predict a specific outcome for just one trial.
If you cannot predict an outcome, what is the point of probability? While you cannot predict the outcome for a single trial, you can predict the pattern of outcomes for a large number of trials, and you can predict the chance of obtaining a particular outcome for a single trial. For example, suppose that a box contains three red balls and seven green balls. If you were blindfolded and selected just one ball – what colour would it be? You cannot guarantee the colour of the selected ball, but the chances are that seven times out of ten the ball would be green.
The ‘probability’ of an event occurring is just the ratio of the number of ways that event can occur, to the total number of possible outcomes. The probability of tossing a coin and getting a HEAD is 1 out of 2, or 0.5. The probability of drawing a HEART from a deck of shuffled bridge cards is 13 out of 52, which reduces to 1 out of 4, or 0.25.
Defined this way, the probability of an event is always a number between zero and one. A probability of zero for an event means that the event will never occur. A probability of 0.33 means the event will occur about one third of the time. A probability of 1.0 means the event will occur every time. Probabilities can be expressed either as fractions or as decimal numbers. The decimal format is usually easier to deal with when several calculations are involved, or a number of probabilities are to be compared.
The ‘odds’ of an event occurring is just the ratio of the number of ways the event can occur, to the number of other possible outcomes. In the example with the three red balls and the seven green balls, the probability of selecting a red ball is 3 out of 10 or 0.3, while the odds of selecting a red ball are 3 to 7. The odds notation is often used when making wagers.
The probability and odds notations emphasize different aspects of the same information. The probability notation has a greater range of application.
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