Probability
Probability (Basic)
Probability describes how likely something is to happen. In probability, an event is the single result of a trial. An outcome is a possible event that results from a trial. The collection of all possible outcomes for a particular trial is called the sample space. For example, when rolling a die, the sample space is the numbers 1 – 6. Rolling a single number, such as 4, would be a single event.
Counting principles are methods used to find the number of possible outcomes for a given situation. The fundamental counting principle states that, for a series of independent events, the number of outcomes can be found by multiplying the number of possible outcomes for each event. For example, if a die is rolled (6 possible outcomes) and a coin is tossed (2 possible outcomes), there are 6 × 2 = 12 total possible outcomes.
The probability of a single event occurring is the number of outcomes in which that event occurs (called favorable events) divided by the number of total possible outcomes.
\(P\ (an\ event) = \frac{number\ of\ favorable\ outcomes}{number\ of\ possible\ outcomes}\)
The probability of any event occurring will always be a fraction or decimal between 0 and 1. A probability may also be expressed as a percent (e.g., a probability of 0.75 is 75%). An event with 0 probability will never occur, and an event with a probability of 1 is certain to occur.
The probability of an event not occurring is referred to as that event’s complement. The sum of an event’s probability and the probability of that event’s complement will always be 1.
To find the probability of multiple independent events—events whose outcomes do not affect each other—multiply the probability of each separate event. For example, the probability of getting the same number on a die during two consecutive rolls is \(\frac{1}{6}×\frac{1}{6} = \frac{1}{36}\).