# Probability

## Probability

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.

Probability explained | Independent and dependent events | Probability and Statistics | Khan Academy

## Examples of Events

Examples of Events:

- tossing a coin and it landing on
*heads* - tossing a coin and it landing on
*tails* - rolling a '3' on a die
- rolling a number > 4 on a die
- it rains two days in a row
- drawing a card from the suit of clubs
- guessing a certain number between 000 and 999 (lottery)

## Certain vs. Uncertain Events

Events that are certain:

- If it is Thursday, the probability that tomorrow is Friday is certain, therefore the probability is 1.
- If you are sixteen, the probability of you turning seventeen on your next birthday is 1. This is a certain event.

Events that are uncertain:

- The probability that tomorrow is Friday if today is Monday is 0.
- The probability that you will be seventeen on your next birthday, if you were just born is 0.

## Outcome Examples

Examples of outcomes:

- When rolling a die for a board game, the outcomes possible are 1,2,3,4,5, and 6.
- The outcomes when choosing the days of a week are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.
- When selecting a door to be chosen behind on the game show "Let's Make a Deal," the outcome of the choices is door 1, door 2, and door 3.

## Probability Examples

The set of all possible outcomes of an experiment is the sample space for the experiment.

- A die is rolled and the number on the top face is recorded. All the integers from 1 to 6 are possible. So
*S*= {1, 2, 3, 4, 5, 6}. - A pair of dice are rolled and the sum of the numbers on the top faces is recorded. The smallest sum is 1 + 1 = 2; the largest is 6 + 6 = 12; and all the integers in-between are possible. So
*S*= {2, 3, 4, ..., 11, 12}.

The two outcomes of tossing a coin are equally likely, which means that each has the same chance of happening. When all outcomes of an event are equally likely, the probability that the event will happen is given by the ration below.

## Equally Likely

These events are equally likely to happen:

- When there is a 50% chance of rain, that means that there a chance that it might rain, but that there is also a chance that it might not rain. These chances are the same so the event is equally likely to happen.
- When one rolls a game die, he/she has exactly the same chance of landing on any of the six sides. Therefore the probability of landing on any one specific side would be 1/6. This is also true for any spinner. Say a spinner is divided into 10 sections. Then there is an equally likely chance that the spinner can land on any of the sections. Thus the probability for the spinner to land in any designated section is 1/10.