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