Probability is a branch of statistics that allows you to calculate how likely something is to happen, and give this likelihood a numerical value. This in turn allows you to make predictions. A event is something that happens, for example tossing a coin. The result of an event is an outcome, for example the coin landing on heads. The probability scale is a scale measuring the likelihood of an outcome. The scale ranges from 0 to 1 with zero described as impossible and 1 described as certainty. The values 0 and 1 are the extremes of probability, and the probability of an outcome occurring can be anywhere between 0 and 1. The point halfway between 0 and 1, 0.5, indicates an event is as likely to happen as not.

The rule for calculating theoretical probability is P(success) = total successful outcomes/total possible outcomes.

For example, if a bag contains 6 red balls and 4 blue balls, the theoretical probability of choosing a blue ball at random is: P(choosing a blue ball) = 4/10 = 2/5. This could be changed to a percentage by dividing the denominator into the numerator,2/50, to obtain 0.4 which is 40%

The rule for calculating experimental probability is: P(success) = total successful outcomes/total events.

For example, a die is thrown 100 times and it lands on 6 a total of 12 times, the experimental probability of throwing the die and landing on a 6 is: P(throwing a 6) = 12/100 = 3/25. This could be changed to a percentage by dividing the denominator into the numerator,3/25, to obtain 0.12 which is 12%

P(Red card) = 26/52

P(Spade) = 13/52

P(King of Club) = 1/52

Therefore the probability of choosing either a red card, a spade, or a King of Club P(R or S or KC) = 26/52 + 13/52 + 1/52 = 40/52 = 10/13 or 80%.

P(4) = 1/6

P(King) = 4/52

P(4 and King) = 1/6 x 4/52 = 4/312 = 1/78 or 1%.

**Theoretical probability**is the probability of an outcome occurring in theory. Theoretical probability is based on equally likely outcomes with no bias or error involved.The rule for calculating theoretical probability is P(success) = total successful outcomes/total possible outcomes.

For example, if a bag contains 6 red balls and 4 blue balls, the theoretical probability of choosing a blue ball at random is: P(choosing a blue ball) = 4/10 = 2/5. This could be changed to a percentage by dividing the denominator into the numerator,2/50, to obtain 0.4 which is 40%

**Experimental probability**is the number of times an outcome occurs in an experiment.The rule for calculating experimental probability is: P(success) = total successful outcomes/total events.

For example, a die is thrown 100 times and it lands on 6 a total of 12 times, the experimental probability of throwing the die and landing on a 6 is: P(throwing a 6) = 12/100 = 3/25. This could be changed to a percentage by dividing the denominator into the numerator,3/25, to obtain 0.12 which is 12%

__Types of Events__**Single event**- An event that involves only one item, for example tossing one coin.**Compound event**- An event that involves more than one item, for example tossing two coins or tossing a coin and rolling a die.**Independent event**- An event that has an outcome which is not affected by any other event. An independent event ia also called a random event. For example, when a die is thrown twice, the change of throwing a particular number on the second occasion is not affected by the first event.**Dependent event**- An event that has an outcome which is affected by another event. For example, if a marble is taken at random form a bag of blue and green marbles, and is not put back into the bag, the color of the second marble to be picked will be dependent on the first event. Example: If there are 3 blue marbles and 3 green marbles in a bag, P(choosing a blue marble) = 3/6 = 1/2 = 50%. If a blue marble is taken out and not replaced, the probability of picking another blue marble is now 2/5 or 40% (as there are only 2 blue marbles and 5 marbles altogether).**Mutually exclusive**- Two or more events that cannot both have successful outcomes at the same time. For example, if A is the event "choosing a red card from a deck of playing cards,, and B is the event "choosing a spade from a deck of playing cards", events A and B are mutually exclusive. You cannot draw a card that meets both criteria. The total probability of a complete set of mutually exclusive events always adds up to 1 or 100%. For example. if there is a 60% chance of rain, there is a 40% chance of no rain. Another example, if the chance of rolling a die and landing on 6 is 1/6 or 16%, then the chance of rolling the die and not landing on 6 is 5/6 or 54%.__Combining probabilities:__**The addition rule:**P(A or B) = P(A) + P(B). The addition rule can be applied to any number of events, as long as they are mutually exclusive. For example, there are 52 cards in a deck of playing cards. There are 26 red cards, 13 spades, and only one King of Clubs. So:P(Red card) = 26/52

P(Spade) = 13/52

P(King of Club) = 1/52

Therefore the probability of choosing either a red card, a spade, or a King of Club P(R or S or KC) = 26/52 + 13/52 + 1/52 = 40/52 = 10/13 or 80%.

**The multiplication rule:**P(A and B) = P(A) x P(B). The multiplication rule can be used to find the probability of a combination of independent or dependent events. For example, to find the probability of throwing a 4 with a die and choosing a king from a deck of cards, use:P(4) = 1/6

P(King) = 4/52

P(4 and King) = 1/6 x 4/52 = 4/312 = 1/78 or 1%.