### Chapter 3. Probability: Randomness

### Random experiments

Probability theory is all about predicting *randomness*. When tossing a coin, one cannot say for certain whether the coin will come up *Heads* or *Tails*. It is possible, however, to calculate the *chances* of something happening or not happening. There is, for example, a #50\%# chance that a fair coin will come up *Heads*.

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Random experiment

**Definition**

A **random experiment** is an experiment or a process of which the outcome cannot be predicted with certainty.

Every experiment has an **outcome***, *which is the result of the experiment.

**Examples**

- Tossing a coin
- Rolling a die
- Drawing a card from a deck

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This course will only consider experiments where *multiple* distinct outcomes are possible. The random experiment of tossing a coin, for example, has #2# possible outcomes: *Heads* and *Tails*.

Similarly, the experiment of tossing a coin twice has #4# possible outcomes:

- (H,T): first
*Heads*, then*Tails* - (T,H): first
*Tails*, then*Heads* - (H,H): two times
*Heads* - (T,T): two times
*Tails*

A common way of depicting the outcomes of a random experiment is with the use of a *tree diagram*.

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Tree diagram

Consider the possible outcomes when a coin is tossed three times. Each coin toss has two possible outcomes: it either comes up *Heads *or it comes up *Tails*.

After #3# tosses, there are #8# possible combinations of outcomes.

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