# Probability

- Probability of an Event
- In the same condition, a random event may occur or may not occur. Can we use a number to express the possibility of an event will occur? When you
throw an unbiased dice once, there are 6 possibilities for a number on top side, that is, 1, or 2, or 3, or 4, or 5, or 6. The possibility of each
number on top side will be equal. The probability of each number on top side will be 1/6 since all possible outcome is 6. The number 1/6 is expressed
as the possibility of each number on top side after throwing an unbiased dice. Generally, the value used to calculate how big a random event A occur
is called the probability of the event A, which is marked as P ( event A ).

- The Value of Probability of an Event
- The probability of an event can be a number from 0 to 1. For an impossible event, its probability is zero. For a certain event, its probability is 1.
The more unlikely an event is, the closer its probability is to 0. The more likely an event is, the closer its probability is to 1.

- Formula of Probability of an Event
- The probability of an event is the ratio of the number of ways that event can occur to the number of all possible outcomes. Note: all possible outcomes are equally likely.

- Summary of the Probability of an Event
- Generally, in a trial, n is the number of all outcome, and they are equally likely, m is the number of ways that event A can occur, then the probability that event A can occur is:

- Example 1
- There are 100 black balls in a box. All balls in the box are same size and same material. If you pick one from the box, what is the probability that the ball you picked is a black ball?

- Answer of Example 1
- Since all balls in the box are black balls, so when you pick one, it is certain a black ball, so the probability that you get a black ball is 1. That is, P ( black ball ) = 1

- Example 2
- There are 8 cards named 1 - 8 on each. All cards are same size and same material. Put all cards in a box and shake it. Then pick one, what is the probability if the card you picked has the number 0 on it?

- Answer of Example 2
- Since all cards named 1 - 8, so there is no card name 0. It is impossible to pick a card with number 0 from the box. So the event to pick a card with 0 is an impossible event. Therefore, the probability to pick a card with number 0 is zero, that is, P ( number 0 ) = 0.