What is Probability? 

Probability is the measure of how likely an event is to occur, expressed as a number between 0 and 1 or 0% and 100%. It is calculated by dividing the number of ways an event can happen by the total number of possible outcomes. For example, the probability of flipping a coin and getting heads is 1 / 2 = one-half or 50% because there is one way to get heads out of two total possible outcomes (heads or tails). 

definitions of probability

Experiment: a repeatable procedure with a set of possible results.

EXAMPLE: Throwing a dice. 

We can throw the dice again and again, so it is repeatable. The set of possible results from any single throw is {1, 2, 3, 4, 5, 6}.

Outcome: A possible result.

EXAMPLE: "6" is one of the outcomes of a throw of a die.

Trial: A single performance of an experiment.

EXAMPLE: I conducted a coin toss experiment. After 4 trials I got these results:

Head - 3 times

Tail - 1 time

Three trials had the outcome "Head", and one trial had the outcome "Tail"

Sample Space: all the possible outcomes of an experiment.

EXAMPLE: Choosing a card from a deck;

There are 52 cards in a deck (not including Jokers)

So the Sample Space is all 52 possible cards: {Ace of Hearts, 2 of Hearts, etc... }

Sample Point: just one of the possible outcomes.

EXAMPLE: Deck of cards;

• the 5 of Clubs is a sample point

• the King of Hearts is a sample point

"King" is not a sample point. There are 4 Kings, so that is 4 different sample points.

Event: one or more outcomes of an experiment.

EXAMPLE: An event can be just one outcome:

• Getting a Tail when tossing a coin

• Rolling a "5"

An event can include more than one outcome:

• Choosing a "King" from a deck of cards (any of the 4 Kings)

• Rolling an "even number" (2, 4 or 6)

what is complementary probability? 

Complementary probability is the probability that an event does not occur, calculated by subtracting the probability of the event from 1.