# Probability of an Event

## Probability of an Event

Ratio of the number of favourable outcomes for an event to the number of possible outcomes, when each outcome has the same number of chances of occurring.

Ratio of the number of elements (favourable outcomes) of an event to the total number of possible outcomes of a random experiment, when each result has just as many chances of occurring.

It is often possible to calculate the theoretical probability of an event. However, sometimes we need to find the experimental or frequential probability.

The theoretical probability of rolling a 6 on a fair six-sided die numbered 1 to 6 is $$\dfrac{1}{6}$$. If we roll the die 600 times, it is almost certain that we will not roll the number 6 exactly 100 times, because it is an experimental probability.

### Examples

• In a random experiment that consists of rolling a fair die with 6 faces numbered 1 to 6, the probability of the event “rolling an even number” has 3 chances out of 6. There are 3 favourable outcomes, which are 2, 4, and 6, out of the six possible outcomes: P(even number) = $$\dfrac{3}{6}$$ = $$\dfrac{1}{2}$$.

• In the random experiment that consists of drawing a ball from a bag that contains 3 red balls, 2 blue balls, and 5 white balls, the probability of the event “drawing a red ball” is 3 chances out of 10. There are 3 favourable outcomes out of 10 possible outcomes: P(red ball) = $$\dfrac{3}{10}$$.